Question

Which expression is equivalent to log5(X/4)^2

Answer 1

Answer: Applying properties of logarithm, the expression equivalent to

log5 (x/4)^2 is: 2 (log5 x - log5 4)

Solution:

log5 (x/4)^2

Using loga b^c = c loga b; with a=5, b=(x/4), and c=2

log5 (x/4)^2 = 2 log5 (x/4)

Using loga (b/c) = loga b - loga c; with a=5, b=x, and c=4

log5 (x/4)^2 = 2 (log5 x - log5 4)

Answer 2

The expression equivalent to the given function is $log_5x^2-log_516$

Law of logarithms

The laws of logarithm that is applicable to the given expression is the product and quotient law.

Given the log expression

$log_5(x/4)^2$

This can be expressed as

$log_5(x^2/16)$

Since quotient becomes subtraction, hence;

$log_5(x^2/16)=log_5x^2-lo_516$

Hence the expression equivalent to the given function is $log_5x^2-log_516$

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