Expand the following log: log_(b) ((x^(3) )/(y^(2) )) SHOW ALL WORK.

Question

Expand the following log:


`log_(b) ((x^(3) )/(y^(2) ))`

SHOW ALL WORK.

Answer 1

`\log_b((x^3)/(y^2) )=3\log_b(x)-2\log_b(y)`

Explanation:

The given logarithmic expression is

`\log_b((x^3)/(y^2) )`

Recall and use the quotient rule of logarithms;

`\log_b(MN)=\log_b(M)-\log_b(N)`;

We apply this property to obtain;

`\log_b((x^3)/(y^2) )=\log_b(x^3)-\log_b(y^2)`

Recall again that;

`\log_b(M^n)=n\log_b(M)`

We apply this property also to obtain;

`\log_b((x^3)/(y^2) )=3\log_b(x)-2\log_b(y)`