Question

Expand the following log:le="log_{3} (x^{4} y)" alt="log_{3} (x^{4} y)" align="absmiddle" class="latex-formula">

SHOW ALL WORK.

Answer 1

Answer:

$\log_{3}(x^4y)=4\log_{3}(x)+\log_{3}(y)$

Step-by-step explanation:

The given logarithmic expression is

$log_{3}(x^4y)$

Recall and use the product property of logarithm: $\log_a(MN)=\log_a(M)+\log_a(N)$;

This implies that;

$\log_{3}(x^4y)=\log_{3}(x^4)+\log_{3}(y)$

Recall again that; $\log_a(M^n)=n\log_a(M)$;

We apply this property to get;

$\log_{3}(x^4y)=4\log_{3}(x)+\log_{3}(y)$