Expand the following log: log_(3) (x^(4) y) SHOW ALL WORK.

Question

Expand the following log:



`log_(3) (x^(4) y)`

SHOW ALL WORK.

Answer 1

`\log_(3)(x^4y)=4\log_(3)(x)+\log_(3)(y)`

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)`