What is 4 log Subscript one-half Baseline w + (2 log Subscript one-half Baseline u minus 3 log Subscript one-half Baseline v) written as a single logarithm? 4 log Subscript one-half Baseline 2 Superscript 4 Baseline u squared minus v cubed

The correct answer is B).

The single solution is [tex]log_\frac{1}{2} \frac{w^{4}u^{2} }{v^{3} }[/tex].

The exponent to which the base of the logarithm should be raised in order to obtain the number N is the logarithm of any number N, if interpreted as an exponential form. Numerous astronomical and scientific calculations involving large numbers can benefit from its use. As an inverse of the exponential function, logarithmic functions are closely related to exponential functions.

Given Equation

[tex]4log_\frac{1}{2} w + (2log_\frac{1}{2} u - 3log_\frac{1}{2} v)[/tex]

[tex]mlog_an = log_an^{m}[/tex]

equation is

[tex]log_\frac{1}{2} w^4 + (log_\frac{1}{2} u^2 - log_\frac{1}{2} v^3)[/tex]

and [tex]log_an - log_am = log_a\frac{n}{m}[/tex]

and [tex]log_an + log_am = log_amn[/tex]

[tex]log_\frac{1}{2} w^4 + (log_\frac{1}{2} \frac{u^2}{v^3} )[/tex]

and [tex]log_\frac{1}{2} \frac{w^{4}u^{2} }{v^{3} }[/tex]

Hence the equation is [tex]log_\frac{1}{2} \frac{w^{4}u^{2} }{v^{3} }[/tex].

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