Question

Given : $\frac{logx}{logy}=\frac{3}{2}$ and $log\left(xy\right)=5$; find the values of $x$ and $y$.

Answer 1

$\frac{logx}{logy}=\frac{3}{2}$

⇒ $logy=\frac{2logx}{3}$ ........... 1

$log\left(xy\right)=5$

⇒$logx+logy=5$ ...... 2

let log x = a


using 1 we get

$a+\frac{2a}{3}=5$

⇒ $3a+2a=15$

⇒ $a=3$

so $logx=3$

⇒ $x={10}^3$

so, x = 1000

so, $logy=2log\frac{x}{3}$

⇒ $logy=2$

$y={10}^2$ = 100