What is the true solution to the equation below? 2 lne^ln2x-lne^ln10x=ln30

Answers

Answer 1

It looks like the equation is

[tex]2\ln\left(e^{\ln(2x)}\right)-\ln\left(e^{\ln(10x)}\right) = \ln(30)[/tex]

Right away, we notice that any solution to this equation must be positive, so x > 0.

For any base b, we have [tex]b^{\log_b(a)}=a[/tex], so we can simplify this to

[tex]2\ln(2x)-\ln\left(10x\right) = \ln(30)[/tex]

Next, [tex]\ln(a^b)=b\ln(a)[/tex], so that

[tex]\ln(2x)^2-\ln\left(10x\right) = \ln(30)[/tex]

[tex]\ln\left(4x^2\right)-\ln\left(10x\right) = \ln(30)[/tex]

Next, [tex]\ln\left(\frac ab\right)=\ln(a)-\ln(b)[/tex], so that

[tex]\ln\left(\dfrac{4x^2}{10x}\right) = \ln(30)[/tex]

For x ≠ 0, we have [tex]\frac xx=1[/tex], so that

[tex]\ln\left(\dfrac{2x}5\right) = \ln(30)[/tex]

Take the antilogarithm of both sides:

[tex]e^{\ln\left((2x)/5\right)} = e^{\ln(30)}[/tex]

[tex]\dfrac{2x}5 = 30[/tex]

Solve for x :

[tex]2x = 150[/tex]

[tex]\boxed{x=75}[/tex]


Related Questions

Anthony read 46 pages of a book in 23 minutes.

To find the unit rate, use
.
Anthony read
pages per minute.

Answers

Answer:

2 pages per minute

Step-by-step explanation:

Take the number of pages and divide by the number of minutes

46 pages / 23 minutes

2 pages per minute

Answer:

2 Pages per Minute

Solutions:

46 ÷ 23 = 2

Final Answer:

Anthony can read 2 pages per minute.

Which one goes where?

Answers

"RS tangent to circle a..." is first statement          Reason: Given

Second Reason: "Radius perpendicular to tangent"

Second Statement: "AR is parrallel to BS"      Reason: "2 lines perpendicular..."

Create truth table to determine whether or not the following statements are logically equivalent

Answers

The statement is totally false.

[tex]\neg P\lor\neg Q \equiv \neg(P \land Q) \not\equiv P\land Q[/tex]

because (P and ¬P) is a contradiction.

What is the explicit formula for the sequence ? -1,0,1,2,3

Answers

Answer:

B

Step-by-step explanation:

substitute the values in the eq. Ot is also arithmetic progression.

Chang has 2 shirts: a white one and a black one. He also has 2 pairs of pants, one blue and one tan. What is the probability, if Chang gets dressed in the dark, that
he winds up wearing the white shirt and tan pants? Show your work.

Answers

Answer:

1/4

Step-by-step explanation:

White = w

Black = B

Blue = b1

Tan = t

Wb1

Wt

Bbi

Bt

The answer will be 1/4, because there are 4 ways it can work and only 1 way it can be white shirt and tan pants.

Answer:

1/4

Step-by-step explanation:

it would be 1/4 because there are 4 different clothing pieces in total and there is only one way it would work the way the problem says.

Cyril has six more than twice as many mangoes as Kubie and half as many mangoes as Maxine. If Kubie has six mangoes, then, in terms of x, how many mangoes do Cyril, Kubie, and Maxine have combined?​

Answers

Answer:

(7x + 18) or 60 Mangoes

Step-by-step explanation:

Let the no. of mangoes Kubie possesses be x

So,

Cyril has mangoes = 2x + 6  ...(i)

So,

Maxine has = 2 * (2x + 6)

= 4x + 12

Given that,

Kubie has mangoes = 6

∵ The combined mangoes they have in terms of x,

= Cyril + Kubie + Maxine

= (2x + 6) + x + (4x + 12)

= 7x + 18

A.T.Q.

Cyril has = 2x + 6

∵ Cyril has mangoes = 2 * (6) + 6

= 18 mangoes

∵ Maxine has = 2 * Cyril's mangoes

= 2 * 18

= 36

Thus,

Total mangoes = Cyril + Kubie + Maxine

= 18 + 6 + 36

= 60 Mangoes

For -180°<θ<0 , which of the primary trigonometric functions may have positive values?

Answers

Answer:

cos theta  = adj / hyp is positive (+/+)

Step-by-step explanation:

In this open interval, the hypotenuse (radius) is always positive, whereas the adjacent side is positive and the opposite side negative.

in this interval:

sin theta = opp / hyp is neg (-/+)

cos theta  = adj / hyp is positive (+/+)

tan theta = opp / adj = (-/+) :  negative

As one once said Another one

Answers

Answer:

f

Step-by-step explanation:

Answer:

S = 62.9

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

tan S = opp side / adj side

tan S = sqrt(42)/ sqrt (11)

tan S = sqrt(42/11)

Taking the inverse tan of each side

tan ^ -1( tan S) =  tan ^-1(sqrt(42/11))

S=62.89816

Rounding to the nearest tenth

S = 62.9

Suppose a rumor is going around a group of 191 people. Initially, only 38 members of the group have heard the rumor, but 3 days later 68 people have heard it. Using a logistic growth model, how many people are expected to have heard the rumor after 6 days total have passed since it was initially spread? (Round your answer to the nearest whole person.)

Answers

Answer:

106 people.

Step-by-step explanation:

Logistic equation:

The logistic equation is given by:

[tex]P(t) = \frac{K}{1+Ae^{-kt}}[/tex]

In which

[tex]A = \frac{K - P_0}{P_0}[/tex]

K is the carrying capacity, k is the growth/decay rate, t is the time and P_0 is the initial value.

Suppose a rumor is going around a group of 191 people. Initially, only 38 members of the group have heard the rumor.

This means that [tex]K = 191, P_0 = 38[/tex], so:

[tex]A = \frac{191 - 38}{38} = 4.03[/tex]

Then

[tex]P(t) = \frac{191}{1+4.03e^{-kt}}[/tex]

3 days later 68 people have heard it.

This means that [tex]P(3) = 68[/tex]. We use this to find k.

[tex]P(t) = \frac{191}{1+4.03e^{-kt}}[/tex]

[tex]68 = \frac{191}{1+4.03e^{-3k}}[/tex]

[tex]68 + 274.04e^{-3k} = 191[/tex]

[tex]e^{-3k} = \frac{191-68}{274.04}[/tex]

[tex]e^{-3k} = 0.4484[/tex]

[tex]\ln{e^{-3k}} = \ln{0.4484}[/tex]

[tex]-3k = \ln{0.4484}[/tex]

[tex]k = -\frac{\ln{0.4484}}{3}[/tex]

[tex]k = 0.2674[/tex]

Then

[tex]P(t) = \frac{191}{1+4.03e^{-0.2674t}}[/tex]

How many people are expected to have heard the rumor after 6 days total have passed since it was initially spread?

This is P(6). So

[tex]P(6) = \frac{191}{1+4.03e^{-0.2674*6}} = 105.52[/tex]

Rounding to the nearest whole number, 106 people.

By selling a radio for $8400 a dealer gained 12% .how much money did she gain​

Answers

Answer:

Amount gained = $900

Step-by-step explanation:

Let the cost price be = x

Given selling price = 8400

And profit% = 12%

Profit = selling price - cost price

        = 8400 - x

[tex]Profit \ \% = \frac{profit}{cost \ price} \times 100\\\\12\% = \frac{8400 - x}{x} \times 100\\\\\ 12 \times \frac{1}{100} = \frac{8400 - x}{x}\\\\\frac{12 \ x}{100} = 8400 - x \\\\\frac{12x}{100} + x = 8400\\\\12x + 100x = 8400 \times 100\\\\112x = 8400 \times 100\\\\x = \frac{8400 \times 100}{112} = 7500[/tex]

Therefore , cost price of the radio $7500

The amount she gained = 8400 - 7500 = $ 900

what is the discrimination of the polynomial below ?
9x2-18x+9

Answers

Answer:

9(x - 1)^2

Step-by-step explanation

9x^2 - 18x + 9

Find the Greatest Common Factor (GCF) in the polynomial

Answer: 9

Then use it to discriminate the polynomial

9(x - 1)^2

The cost of producing a custom-made clock includes an initial set-up fee of $1,200 plus an additional $20 per unit made. Each clock sells for $60. Find the number of clocks that must be produced and sold for the costs to equal the revenue generated. (Enter a numerical value.)

Answers

Answer:

30 clocks

Step-by-step explanation:

Set up an equation:

Variable x = number of clocks

1200 + 20x = 60x

Isolate variable x:

1200 = 60x - 20x

1200 = 40x

Divide both sides by 40:

30 = x

Check your work:

1200 + 20(30) = 60(30)

1200 + 600 = 1800

1800 = 1800

Correct!

Please help with this question

Answers

Answer:

im not too sure but try using a cartesuan plane and measure it precisely using a protractor then key in the measurements. Im not entirely sure its the correct method tho

khai niem hinh cat don gian ?

Answers

Answer:

khai niem hinh cat don gian?

A consumer electronics company is comparing the brightness of two different types of picture tubes for use in its television sets. Tube type A has mean brightness of 100 and standard deviation of 16, and tube type B has unknown mean brightness, but the standard deviation is assumed to be identical to that for type A. A random sample of tubes of each type is selected, and is computed. If equals or exceeds , the manufacturer would like to adopt type B for use. The observed difference is . a. What is the probability that exceeds by 3.0 or more if and are equal

Answers

Answer:

The answer is "0.7794".

Step-by-step explanation:

Please find the complete question in the attached file.

Given:

[tex]\to n_{1}=n_{2}=25\\\\[/tex]

Hypotheses:

[tex]\to H_{0}:\mu_{B}-\mu_{A}\geq 0\\\\\to H_{a}:\mu_{B}-\mu_{A}< 0\\\\[/tex]

Testing statistics:

[tex]\to z=\frac{(\bar{x}_{B}-\bar{x}_{A})-(\mu_{B}-\mu_{A})}{\sqrt{\frac{\sigma^{2}_{B}}{n_{1}}+\frac{\sigma^{2}_{A}}{n_{2}}}}=\frac{3.5-(0)}{\sqrt{\frac{16^{2}}{25}+\frac{16^{2}}{25}}}=0.77[/tex]

The test is done just so the p-value of a test is

[tex]\to p-value = P(z < 0.77) = 0.7794[/tex]

Because the p-value of the management is large, type B can take it.

y
27
х
10
11
12
In order for the data in the table to represent a linear
, function with a rate of change of -8, what must be the
value of a?
a
11
O a = 2
O a = 3
O a = 19
a = 35

Answers

It’s c for sure only because I had it on a test

The value of a that would make the data in the table represent a linear function with a rate of change of -8 is a = 19.

Option D is the correct answer.

What is a function?

A function has an input and an output.

A function can be one-to-one or onto one.

It simply indicated the relationships between the input and the output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

The rate of change of a linear function is also known as the slope of the function.

To determine the slope of the function represented by the given table, we need to calculate the change in Y for a unit change in X.

Using the values given in the table, we can calculate the slope as follows:

Slope = (Change in Y) / (Change in X)

So,

(a - 27) / (11 - 10) = (11 - 27) / (12 - 10) = -8

Setting this equation equal to -8, we get:

= (a - 27) / 1

= -8

Simplifying the equation, we get:

a - 27 = -8

a = 19

Therefore,

The value of a that would make the data in the table represent a linear function with a rate of change of -8 is a = 19.

Learn more about functions here:

https://brainly.com/question/28533782

#SPJ7

An isosceles trapezoid has a consecutive-sides of length: 10,6,10 and 14. Find the measure of each angle if the trapezoid.

Answers

Answer:

Angle A = Angle D = 69° 30'

Angle B = Angle C = 110° 30'

Step-by-step explanation:

     B ___ C

    /              \

  /                  \

A ________ D

AB and CD are 10

BC is 6

AD is 14

If we divide the trapezoid, we can imagine a line.

     B_ F_C

    /      |      \

  /        |         \

A ___E____ D

AE = ED = 7 (14/2)

BF = FC = 3

So now, we draw another line from B or C to AE or ED

     B_ F_ C

    /      |     | \

  /        |     |    \

A ___E_ G_ D

EG = GD = 3.5 (7/2)

There is a right triangle now, GCD

GD is 3.5 and CD is 10. To determine angle D, we can apply trigonometric function:

CD is H, and GD is A

cos D = A/H

cos D = 3.5/10 → 0.35

angle D = 69° 30'

By theory, we know that angle D and angle A, are the same so:

Angle D = Angle A = 69° 30'

Angle B = Angle C

We also make a cuadrilateral, which is EFCD.

Angle D is 69° 30', Angle E is 90°, Angle F is also 90°

Sum of angles in cuadrilateral is 360°

360° - 69° 30' - 90° - 90° = Angle C = Angle B

Angle C = Angle B = 110° 30'

Let's confirm the angles in the trapezoid:

69° 30' + 110° 30' + 69° 30' + 110° 30' = 360°

A + B + C + D

the adjacent sides of a parallelogram are (x + 3) and (x + 2). Find the perimeter of the parallelogram

Answers

9514 1404 393

Answer:

  4x+10

Step-by-step explanation:

For parallelogram adjacent sides a and b, the perimeter is ...

  P = 2(a +b)

For the given sides, the perimeter is ...

  P = 2((x +3) +(x +2)) = 2(2x +5)

  P = 4x +10 . . . perimeter of the parallelogram

Please help with this question

Answers

9514 1404 393

Answer:

  (d)  -1/32

Step-by-step explanation:

It may be easier to rearrange the expression so it has positive exponents.

  [tex]\dfrac{1}{2^{-2}x^{-3}y^5}=\dfrac{2^2x^3}{y^5}=\dfrac{4(2)^3}{(-4)^5}=-\dfrac{4\cdot8}{1024}=\boxed{-\dfrac{1}{32}}[/tex]

Determine the domain and range of the graph

Answers

Answer:

5 ≤ x ≤ 10             5 ≤ y ≥ -1

Step-by-step explanation:

hope anyone help me please​

Answers

9514 1404 393

Answer:

  a) Lahulspiti: -8; Srinigar: -2; Shimla: 5; Ooty: 14; Bengahuru: 22

  b) 30

  c) 6

  d) yes; no

Step-by-step explanation:

a) The values are read from the graph.

__

b) 22 -(-8) = 22 +8 = 30 . . . . difference between highest and lowest

__

c) -2 -(-8) = -2 +8 = 6 . . . positive difference

(Technically, the difference between L and S is L - S = (-8) -(-2) = -6.)

__

d) -2 + 5 < 5 . . . . true

  -2 + 5 < -2 . . . . false

E. The ratio of monthly income to savings of a family is 7:2. If the savings is Rs. 500, find the monthly income and expenditure.​

Answers

Step-by-step explanation:

Since the ratio of monthly income to savings of the family is 7:2, we assume that the income be 7t and savings be 2t

Now, we are given that the savings is =Rs 500

So, According to our assumption, 2t=500

⇒t=250

Hence, the income of the family is =7×250=Rs 1750

And the expenditure is =Income−Savings

=Rs 1750−Rs 500

=Rs 1250

Perimeter (numerical) cm

Answers

Answer:

101 cm

Step-by-step explanation:

Add all the side lengths up to get 101 cm.

A chemist has three different acid solutions.

The first solution contains 25% acid, the second contains 35%acid, and the third contains 55% acid.
She created 120 liters of a 40% acid mixture, using all three solutions. The number of liters of 55% solution used is 3 times the number of liters of 35% solution used.

How many liters of each solution was used?

Answers

Let x, y, and z be the amounts (in liters, L) of the 25%, 35%, and 55% solutions that the chemist used.

She ended up with 120 L of solution, so

x + y + z = 120 … … … [1]

x L of 25% acid solution contains 0.25x L of acid. Similarly, y L of 35% solution contains 0.35y L of acid, and z L of 55% solution contains 0.55z L of acid. The concentration of the new solution is 40%, so that it contains 0.40 (120 L) = 48 L of acid, which means

0.25x + 0.35y + 0.55z = 48 … … … [2]

Lastly,

z = 3y … … … [3]

since the chemist used 3 times as much of the 55% solution as she did the 35% solution.

Substitute equation [3] into equations [1] and [2] to eliminate z :

x + y + 3y = 120

x + 4y = 120 … … … [4]

0.25x + 0.35y + 0.55 (3y) = 48

0.25x + 2y = 48 … … … [5]

Multiply through equation [5] by -2 and add that to [4] to eliminate y and solve for x :

(x + 4y) - 2 (0.25x + 2y) = 120 - 2 (48)

0.5x = 24

x = 48

Solve for y :

x + 4y = 120

4y = 72

y = 18

Solve for z :

z = 3y

z = 54

If $6^x = 5,$ find $6^{3x+2}$.

Answers

If 6ˣ = 5, then

(6ˣ)³ = 6³ˣ = 5³ = 125,

and

6³ˣ⁺² = 6³ˣ × 6² = 125 × 6² = 125 × 36 = 4500

Suppose the method of tree ring dating gave the following dates A.D. for an archaeological excavation site. Assume that the population of x values has an approximately normal distribution.

1241 1210 1267 1314 1211 1299 1246 1280 1291

a. Determine if the data meets the initial conditions to construct a confidence interval.
b. Find the sample mean year x and sample standard deviation σ.
c. What is the maximal margin of error when finding a 90 % confidence interval for the mean of all tree-ring dates from this archaeological site?

Answers

Answer:

(1238.845 ;1285.376)

Step-by-step explanation:

Conditions for constructing a confidence interval :

Data must be random

Distribution should be normal and independent ;

Based on the conditions above ; data meets initial conditions ;

C. I = sample mean ± margin of error

Given the data :

1241 1210 1267 1314 1211 1299 1246 1280 1291

Mean, xbar = Σx / n = 11359 / 9 = 1262.11

The standard deviation, s = [√Σ(x - xbar)²/n - 1]

Using a calculator ; s = 37.525

The confidence interval :

C.I = xbar ± [Tcritical * s/√n]

Tcritical(0.10 ; df = n - 1 = 9 - 1 = 8)

Tcritical at 90% = 1.860

C. I = 1262.11 ± [1.860 * 37.525/√9]

C.I = 1262.11 ± 23.266

(1238.845 ;1285.376)

± 23.266

The margin of error :

[Tcritical * s/√n]

[1.860 * 37.525/√9]

C.I = ± 23.266

PLEASE HELP WILL MARK BRAINLIEST

Answers

9514 1404 393

Answer:

  x = 10/3 = 3 1/3 ≈ 3.33

Step-by-step explanation:

Triangles ABC and ADE are similar, so corresponding sides are proportional.

  DE/DA = BC/BA

  x/(4+6) = 2/6

  x = 10(2/6) = 10/3 = 3 1/3

find and sketch the domain of the function. f(x,y)=√(4-x^2-y^2) +√(1-x^2)

Answers

Answer:

Hello

Step-by-step explanation:

The domain is limited with 2 lines parallel: -1 ≤ x ≤ 1

and the disk ? (inside of a circle) of center (0,0) and radius 2

[tex]dom\ f(x,y)=\{(x,y) \in \mathbb{R} ^2 | \ -1\leq x \leq -1\ and \ ( -\sqrt{4-x^2} \leq \ y \leq \sqrt{4-x^2}\ ) \ \}\\[/tex]

Suppose point (4, −9) is translated according to the rule (, ) → ( + 3, − 2). What are the coordinates of ′? Explain

Answers

Answer: I’m sorry I just need points..

HELP ASAP PLEASE! I tried inputting the numbers into the standard deviation equation but I did not get the right answer to find z. Can someone please help me? Thank you for your time!

Answers

Answer:

Z =  -1.60

it is low ... it appears that for this problem 2 standard deviations below must be reached to be considered "unusual"

Step-by-step explanation:

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A standard deck of 52 cards has 13 ranks (Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King) and 4 suits ($\spadesuit$, $\heartsuit$, $\diamondsuit$, and $\clubsuit$), such that there is exactly one card for any given rank and suit. Two of the suits ($\spadesuit$ and $\clubsuit$) are black and the other two suits ($\heartsuit$ and $\diamondsuit$) are red. The deck is randomly arranged. What is the probability that the top card is a 3 and the second card is an eight A 34-m length of wire is stretched horizontally between two vertical posts. The wire carries a current of 68 A and experiences a magnetic force of 0.16 N. Find the magnitude of the earth's magnetic field at the location of the wire, assuming the field makes an angle of 72.0 with respect to the wire. Calculate the maximum absolute uncertainty for R if:R = 9A / BA = 32 +/- 2 secondsB = 11 +/- 3 seconds1 second0.33 seconds9 seconds2 seconds6 seconds Humans are diploid; every individual carries only two alleles.a. Trueb. False HELP PLEASE, Function problem please help me!!!!!!!!!!!! What is the mass of a piece of iron if its density is 1.98 g/mL and its volume is 2.45 mL?0.80 g4.8581.2485.9982.71 g Find the intercepts of the function y = 3x + 9 Which are characteristics of a video with a higherbit rate? Choose all that apply.fewer frames per secondmore frames per secondlower qualityhigher qualitylarger file sizesmaller file size distance of distinct vision.is placed at a distance less than the distance of near point, its image owill be blurred. Hence human eye can not see such object clearly.ADDITIONAL INFORMATIONdistance of distinct vision for a normal eye of different age groupsBabies = 7 cmAdults = 25 cmerson of age 55 years and above = 100 cmever, in our discussion we are concerned with a normal eye of an adult so leastThe foulart position of an ahiect from a human eve so that the sh The first side of a triangle measures 5 in. less than the second side, the third side is 3 in. more than the first side, and the perimeter is 17 in. Set up an equation that relates the sides of the triangles in terms of the perimeter of the triangle.3s - 10 = 173s - 7 = 172s -7 = 172s - 5 = 17 There are 3 pizzas. Each child will get 1/2 of the pizza. How many 1/2's will there be in 3 pizzas? a)What are the expected returns and standard deviations of a portfolio consisting of:1.100 percent in stock A If a mutation occurs in the coding sequence of a gene, what types ofissues might happen?Select one:A) All of these answers.B) The gene could be expressed in the wrong cell.C) The gene could be unaffected.D) The gene could be permanently broken. Geographically India is a________ How did Japan gain territory and control of areas of China during WW1? Which provides the best example of someone negatively affecting their own time management?A. Anita welcomes unscheduled visits throughout the day and enjoys them as surprise breaks.B. Brix sets specific personal goals for each week that are separate from the "to do" list.C. Oden sets aside a few hours each month to document how long tasks usually take to complete.D. Samir thinks the term paper is going to take 10 hours but budgets for 12 instead. What happens to a glass of sugar solution when sugar is added to it? The number of moles of water increases. The number of moles of water decreases. The molarity of the solution increases. The molarity of the solution decreases. How much work does the electric field do in moving a proton from a point with a potential of 170 V to a point where it is -50 V Suppose you buy some stock in the Alpha Corporation at a price of $45.95 per share. 410 days later you sell the stock for $48.27. During this period you received a per share dividend of $1.20. What is your annualized return on this investment