Question

Find the value of x (3/5)^x(5/3)^2x=125/27​

Answer 1

Given:

The equation is

$\left(\dfrac{3}{5}\right)^x\left(\dfrac{5}{3}\right)^{2x}=\dfrac{125}{27}$

To find:

The value of x.

Solution:

We have,

$\left(\dfrac{3}{5}\right)^x\left(\dfrac{5}{3}\right)^{2x}=\dfrac{125}{27}$

$\left(\dfrac{5}{3}\right)^{-x}\left(\dfrac{5}{3}\right)^{2x}=\dfrac{5\times 5\times 5}{3\times 3\times 3}$      $[\because \left(\dfrac{a}{b}\right)^{-m}=\left(\dfrac{b}{a}\right)^{m}]$

$\left(\dfrac{5}{3}\right)^{-x+2x}=\dfrac{5^3}{3^3}$          $[\because a^ma^n=a^{m+n}]$

$\left(\dfrac{5}{3}\right)^{x}=\left(\dfrac{5}{3}\right)^{3}$

On comparing the exponents, we get

$x=3$

Therefore, the value of x is 3.