Question

Find the numerical value of the log expression.

Answer 1

The final value of the given log expression is -28

Logarithm functions

Logarithm functions are inverse of exponential functions. Given the log expression below;

$log\frac{c^5}{\sqrt{b^3}}$

Given the following parameters

log a = 6

log b = -10

log c = -8

The log expression can be expressed as:

$log\frac{c^5}{\sqrt{b^3}}=logc^5-log(\sqrt{ab^3})\\log\frac{c^5}{\sqrt{b^3}}=5logc-(1/2loga +3/2logb)\\log\frac{c^5}{\sqrt{b^3}}=5(-8)-(1/2(6)+3/2(-10))\\log\frac{c^5}{\sqrt{b^3}}=-40-(3-15)\\log\frac{c^5}{\sqrt{b^3}}=-40+12\\log\frac{c^5}{\sqrt{b^3}}=-28$

Hence the final value of the given log expression is -28

Learn more on log function here: brainly.com/question/13473114

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