Question

Expand the following log:

$log_{b} (\frac{x^{3} }{y^{2} })$

SHOW ALL WORK.

Answer 1

Answer:

$\log_b(\frac{x^3}{y^2} )=3\log_b(x)-2\log_b(y)$

Step-by-step explanation:

The given logarithmic expression is

$\log_b(\frac{x^3}{y^2} )$

Recall and use the quotient rule of logarithms;

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

We apply this property to obtain;

$\log_b(\frac{x^3}{y^2} )=\log_b(x^3)-\log_b(y^2)$

Recall again that;

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

We apply this property also to obtain;

$\log_b(\frac{x^3}{y^2} )=3\log_b(x)-2\log_b(y)$