Without using logarithm tables, find value of x in the equation:
log x³+ log5x =5log2-log⅖​

Answers

Answer 1

Answer:

[tex]x =2[/tex]

Step-by-step explanation:

Given

[tex]\log x\³+ \log5x =5\log2-\log\frac{2}{5}[/tex]

Required

Find x

We have:

[tex]\log x\³+ \log5x =5\log2-\log\frac{2}{5}[/tex]

Apply exponent rule

[tex]\log x\³+ \log5x =\log2^5-\log\frac{2}{5}[/tex]

[tex]\log x\³+ \log5x =\log32 -\log\frac{2}{5}[/tex]

Apply product and quotient rules of logarithm

[tex]\log (x\³* 5x) =\log(32 \div \frac{2}{5})[/tex]

[tex]\log (5x^4) =\log(80)[/tex]

Cancel log on both sides

[tex]5x^4 = 80[/tex]

Divide by 5

[tex]x^4 = 16[/tex]

Take 4th roots of both sides

[tex]x =2[/tex]


Related Questions

Vectors a = (1,0) and b= (1,1) are given. For what λ vector a + λb is perpendicular to vector a?

Answers

Answer:

-1

Step-by-step explanation:

Vector a=(1,0) if visualized as a line has points (0,0) and (1,0). This means the line is horizontal and has equation y=0.

This means we are looking for a vertical line.

Instead of lambda, I'm going to use u.

So we want a+ub=(1,0)+u(1,1). to vertical. If we visualize this as a line with points (0,0) and (1+u,u). We would need u=-1 so this would be vertical.

So vectors a=(1,0) and a+ub=(1,0)+u(1,1) are perpendicular for u=-1.

So we are saying vectors (1,0) and (0,-1) are perpendicular. If you draw these, you can get a visual confirmation.

The value of λ is -1 and is perpendicular to vector a.

What is Vector?

A vector is a number or phenomena with two distinct properties: magnitude and direction. The term can also refer to a quantity's mathematical or geometrical representation. In nature, vectors include velocity, momentum, force, electromagnetic fields, and weight.

We have,

Vector a = (1, 0) and b = (1, 1).

Here the vector is visualized as line is horizontal and has equation y=0.

Now, we have a + λb is perpendicular to vector a.

So, a + λb = (1, 0) + λ(1, 1)

                 = (1 + λ, 1)

Now, to get the vertical component we must have λ= -1.

Then, a(1, 0) and a+λb= (1,0)+ λ(1, ) are perpendicular to λ=-1.

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SOMEONE HELP ME PLEASE

Answers

Answer:

Step-by-step on:ơ

For which of the following do you need to change the final y to i before adding the suffix?


say + -ing


happy + -ness


enjoy + -ment


play + -er

Answers

The answer to this question would be the second option. It’s not happyness but it is happiness. :)

In ΔABC, ∠A = 50° and the external bisectors of ∠B and ∠C meet at O as shown in figure. The measure of ∠BOC is

Answers

Answer:

17

Step-by-step explanation:

Look at Triangle ABC, The rays meet at line BC and they are both from the interior point A. So this means that AB=AC. This makes ABC a isosceles triangle. Using the isosceles triangle theorem, Angle B and Angle C measure is equal to each other so

[tex]50 + x + x = 180[/tex]

[tex]50 + 2x = 180[/tex]

[tex]2x = 130[/tex]

[tex]x = 65[/tex]

This means angle b and C of the triangle ABC measure is 65.

External bisector bisect a figure that it makes the original angle split into half that they are equal to each other.

This means the angle below Angle B and angle C measure is 32.5. We can find the measure of Angle B and C in triangle BOC. This is a isosceles triangle as well so

[tex]32.5 + 65 + x = 180[/tex]

[tex]98.5 + x = 180[/tex]

[tex]x = 81.5[/tex]

Angle C is 81.5 as well so

[tex]81.5 + 81.5 = 163[/tex]

Find angle o

[tex]180 - 163 = 17[/tex]


What is the surface area of the right prism?
92 ft2
46 ft2
48 ft2
70 ft2

(will mark brainliest <3)

Answers

Answer:  70 ft^2   ( choice D )

=========================================================

Work Shown:

L = 8 ft = lengthW = 3 ft = widthH = 1 ft = height

SA = surface area of the rectangular prism (aka block or box)

SA = 2*(LW + LH + WH)

SA = 2*(8*3 + 8*1 + 3*1)

SA = 2*(24 + 8 + 3)

SA = 2*(35)

SA = 70 square feet

This is the amount of wrapping paper you would need to cover all six sides of the box. This assumes that there are no gaps or overlaps.

Which expressions are equivalent to 5+(-3)(6x-5)5+(−3)(6x−5)5, plus, left parenthesis, minus, 3, right parenthesis, left parenthesis, 6, x, minus, 5, right parenthesis ? Choose all answers that apply: Choose all answers that apply: (Choice A) A 18x-2018x−2018, x, minus, 20 (Choice B) B 3x-33x−33, x, minus, 3 (Choice C) C None of the above

Answers

5+(-18x+15)5 + (-18x +15)5

5+ (-90x +75) + (-90x + 75)

-180x +155

let's see the alternatives:

a) -2000x - 2018 -> -200x - 201,8

b) -30x - 33 -> -180x -198

c) none of the above

so, c is the right one

hope it helps :)

Answer:

ITS C

Step-by-step explanation:

Select the two values of x that are roots of this equatio 2x - 5 = - 3x ^ 2

Answers

alright I can help!

so to find the two values of x that are roots of the equation we need to put the variables all on one side so that we can set up the quadratic formula.

3x^2+2x-5=0 (the -3x^2 becomes positive when moved across the equal sign)

now we can set up the quadratic formula. the equation is x= (-b+-(sqrt of b^2 -4ac))/ 2a

so now we just plug in our variables.

x= (-2+-(sqrt of 2^2 -4×3×-5))/ 2×3

x= (-2+-8)/6

now we just seperate the equations so that we have the two roots. and then just solve!

x= (-2-8)/6 -> x= -5/3

x= (-2+8)/6 -> x=1

hope this helps! best wishes and best of luck!!

Find the missing value that makes each of the following pairs of fractions equivalent.
3/5 = [] 20
4/7 = 16 []
25/30 = []6
4 = (1/10
Circle the improper fractions
9/5
5/12
21/8
11/19
10/1

Answers

Answer:

3/5=12/20 multiply by 4

4/7=16/49 a square of

25/30=5/6 divide with 5

improper fractions

9/5

21/8

10/1

Let g(x) = f (x+1) - 2, find when g(x) = 12

I don't know how to evaluate this since I have both g(x) and an f(x).

Answers

Answer:

f(x +1 ) =14

Step-by-step explanation:

12= f(x +1) -2

f(x +1) = 12 +2

f (x+1 ) = 12

Suppose h” is continuous at x = 2,h' (2) = 0, and h” (2) < 0.
What can you say about the behavior of h at X = 2?

Answers

Answer:

Hello,

Step-by-step explanation:

h(x) has a minimum at x=  2. (h(x) is turning down at x=2)

I have suppose that h''(2 + ) <0 and h''(2 -) <0

Please help 15 points! And brainlist! Hurry I need help right now!

Answers

Answer: quadrant 1

Step-by-step explanation:

the triangle will make 5 360° rotations and then one 180° rotation. we know this because 1980/360=5.5

An employee is scheduled to work 40 hours per week at a base rate of $18.50 per hour. In addition to the 40 scheduled hours, the employee is asked to work 8 hours of overtime for one week due to staffing shortages. If overtime is paid at a rate of 1.5 times the base rate, how much will the employee earn for the week? (use $xxx.Xx format)

Answers

Answer:

$962.00

Step-by-step explanation:

We can start from the first sentence of the word problem and work from there.

First, the employee is working for 40 hours at $18.50 per hour. This means that for each hour, the employee is gaining $18.50 . This can be represented as $18.50 * 40 = $740 for their base pay.

Next, the employee works 8 hours of overtime at 1.5 * base pay (18.50). For each hour of overtime they work, they earn 1.5 * 18.50 = $27.75 dollars. Their earnings from overtime work for the week can be represented as

8 * 27.75 = $222

Because all the employee's hours are encompassed in overtime and base pay, we can add the two together to get

740 + 222 = $962.00 for their total pay for the week

Please help me out with my maths I would really appreciate it ​

Answers

Answer:

a.

1. The rule in this sequence is (+5) every next pattern

2. 22, 27, 32, 37

3. 42

4. 12 term

5. 67

b.

1. The rule in this sequence is (-3) every next pattern

2. -7, -10, -13, -16

3. -16

4. 13 term

5. -37

Step-by-step explanation:

Answer:

I'm not sure about the answer.

a.

1. The rule in this sequence is (+5) every next pattern

2. 22, 27, 32, 37

3. 42

4. 12 term

5. 67

b.

1. The rule in this sequence is (-3) every next pattern

2. -7, -10, -13, -16

3. -16

4. 13 term

5. -37

Hope this helps you ^^

In a 4-digit perfect square, the first two digits are the same, and the last two digits are also the same. What is the value of this 4-digit number?

Answers

Answer:

7744

Step-by-step explanation:

Let the number is in the form of aabb.

We can put it as:

aabb = 11*(100a + b) = 11*(99a + a + b)

The number is a perfect square so it must be divisible by 11.

It is divisible by 11 if (a + b) is divisible by 11..

On the other hand, b = 0, 1, 4, 5, 6, 9 as the last digit of a perfect square.

Also, both a and b must be within (0,9) interval.

Considering the above conditions we have options:

a,b = 2,9 or 5,6 or 6,5 or 7,4

The numbers are:

2299556666557744

By testing we confirm only one of them is a perfect square:

7744

Five children share 24m of ribbon equally.
How much ribbon will each child get?
Write your answer as a mixed number.

Answers

Answer: 4 8/10m

Explanation:

Total Ribbon = 24m

Total children = 5

Ribbon each student gets = 24÷5

= 4.8

Now 4.8 = 48/10

4 8/10m is the mixed fraction

So each child will get 4 8/10m ribbon

Must click thanks and mark brainliest

If five children share 24m of ribbon equally then each children gets [tex]4\frac{4}{5}[/tex] of ribbon.

What is Division?

A division is a process of splitting a specific amount into equal parts.

Given that five children share 24m of ribbon equally.

We have to find the amount of ribbon each children gets.

To find this we have to divide the length of the ribbon with the number of children.

Twenty four divided by five.

24 is the dividend and five will be the divisor

24/5

Now we have to write this in mixed fraction

[tex]4\frac{4}{5}[/tex]

Hence, if five children share 24m of ribbon equally then each children gets [tex]4\frac{4}{5}[/tex] of ribbon.

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Ian drives an electric car. He can drive 425 kilometres before he needs to stop and recharge his car. It takes 10 minutes to charge 50 kilometres. How long does Ian have to wait for his car to fully charge?

Answers

Answer:

85 minutes

Step-by-step explanation:

425/50=8.5 10 minute increments

8.5*10= 85 minutes

which statement is true

Answers

3) an $8 delivery fee and $1.50 per litre of water

This is because the $8 is a constant baseline, then adding $1.50 times the amount of litres purchased.

Boston wheel chair marathon how long would it take to run a 30 mile race

Answers

G all please come to mpu-xcny-did

Fill in the missing number in the equation.

Drop down answers: -2, 8, 15, or It is not possible to find the answer

Answers

9514 1404 393

Answer:

  8

Step-by-step explanation:

The matrix being multiplied is the same in all cases, so we can "collect terms" in the usual way.

  3A +5A = (3+5)A = 8A . . . . . . where A represents the 2×2 matrix

The missing number is 8.

which one of the following has a terminating decimal expansion?
a.5/64
b.8/9
c.14/15
d.1/12​

Answers

Answer:

b. 8/9

Step-by-step explanation:

step by step explanation

Answer:

A

Step-by-step explanation:

Because if you were to out each fraction into a calculator you see that b,c, and d have a never ending decimal. The only fraction that does end in option A, therefore ur answer is option a

Solve for the value of n.
n =

Answers

Answer:

136+(4n-8)=180

136+4n-8=180

4n+128=180

4n=52

n=13

Step-by-step explanation:

please mark me as brainliest

The answer is n=13 hope that helps

find the missing side​

Answers

Answer:

x ≈ 13.7

Step-by-step explanation:

Using the cosine ratio in the right triangle

cos70° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{x}{40}[/tex] ( multiply both sides by 40 )

40 × cos70° = x , then

x ≈ 13.7 ( to the nearest tenth )

16x + 90 = 2 ( 10x + 5 ) answer

Answers

Answer:

x = 20

Step-by-step explanation:

[tex]16x+90=2(10x+5)\\\\16x+90=20x+10\\\\90=4x+10\\\\80=4x\\\\20=x[/tex]

Which of the following rules describes the function graphed below?

Answers

Answer:

D

Step-by-step explanation:

Output = 3*input - 2. Observe the graph again

Which property does the following statement illustrate? (a+b)c = (b+a)c

A: associative
B: Commutative
C: Identity
D: None

Answers

I believe the answer is b I think

PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER PLS GIVE ME A STEP BY STEP EXPLANATION!!
Larry is going on a road trip for work. He is recording how many miles he drives, and how many gallons of gas he uses for his expense report. Which is the independent variable?

A. the amount of miles Larry drives
B. the type of roads Larry drives on
C. the type of car Larry drives
D. the amount of gasoline Larry uses

Answers

My best guess would be that the independent variable is A. the amount of miles Larry drives.
An independent variable is one that isn't changed by the other variables you are trying to measure.
The amount of miles Larry drives doesn’t depend on anything in this situation.
The question only mentions gallons of gas and miles so I would think you disregard the type of roads Larry drives on and type of car Larry drives.
The amount of gasoline Larry uses is a dependent variable because it depends on the amount of miles Larry drives.
Hope this helps

[(-33) + 46 + 68] - |15 - 61|

Answers

Answer:

127

Step-by-step explanation:

[(-33) + 46 + 68] - (15 - 61)

(114-33)-(-46)

81+46

127

find the coefficient of mt in the expansion of 4m(3n-2t)+3t(3t-2m)​

Answers

Answer:

-14

Step-by-step explanation:

12mn-8mt+9t²-6mt

12mn+9t²-14mt

the coefficient of mt is -14

The coefficient of the given expansion 4m(3n-2t)+3t(3t-2m)​ will be -14.

What is expansion?

Expanded form is the term used in mathematics to refer to the process of expanding a number to convey the value of every digit and place value.

When a mathematical object is increased by a multiplier that is bigger in actual values than one, an expansion follows.

In another word, if you solve a factor by opening the bracket then you will go to get on some expanded term called expansion.

In mathematics, all real-life problems can be converted into equations which are sometimes in form of factors and we need to expand them to create solutions.

Given that

⇒ 4m(3n-2t)+3t(3t-2m)​

⇒  12mn -8mt + 9t² - 6mt

⇒  12mn + 9t² + 14 mt

Hence it's clear that the coefficient of mt will be -14.

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Hey I want to make sure my answer for this question is right I think the answer is A but I want to e sure I did it right ༼ つ ◕_◕ ༽つ

Answers

Answer:

The correct choice is option C. 4xy√3y

Step-by-step explanation:

√12x^2y^3 + 2xy√3y

√12x^2y^3 = 2√3 xy√y

2xy√3y = 2√3 xy√y

2√3 xy√y +  2√3 xy√y

= 4√3 xy√y

= 4xy√3y

Help Pls if you want!!!!

Answers

Answer:

Its 2.5 percent ladd enjoy

Step-by-step explanation:

Answer:

2 per team and 2 left

Step-by-step explanation:

10 can't split into 4 evenly so, you can only give 2 to each team causing there to be 2 left.

4*2 = 8

10-8 = 2

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