Question

If $\log x^2{y}^3=a$ and $\log \frac{x}{y}=b$, then $\frac{\log x}{\log y}$ is equal to _____________.

• A. $\frac{a-2b}{a+3b}$
• B. $\frac{a+2b}{a-3b}$
• C. $\frac{a+3b}{a-2b}$
• D. $\frac{a-3b}{a+2b}$

Answer 1

Answer: (C)

$\frac{a+3b}{a-2b}$

Given$log{x}^2{y}^3=a$

$log{x}^2+log{y}^3=a$

$2logx+3logy=a$

$log\frac{x}{y}=b$

$logx-logy=b$

Solving both the equations we get

$logx=\frac{a+3b}{5}$

and $logy=\frac{a-2b}{5}$

$\frac{logx}{logy}=\frac{a+3b}{a-2b}$