Question

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

Answer 1

Given:

The equation is

`\left((3)/(5)\right)^x\left((5)/(3)\right)^(2x)=(125)/(27)`

To find:

The value of x.

Solution:

We have,

`\left((3)/(5)\right)^x\left((5)/(3)\right)^(2x)=(125)/(27)`

`\left((5)/(3)\right)^(-x)\left((5)/(3)\right)^(2x)=(5* 5* 5)/(3* 3* 3)`
`[\because \left((a)/(b)\right)^(-m)=\left((b)/(a)\right)^(m)]`

`\left((5)/(3)\right)^(-x+2x)=(5^3)/(3^3)`
`[\because a^ma^n=a^(m+n)]`

`\left((5)/(3)\right)^(x)=\left((5)/(3)\right)^(3)`

On comparing the exponents, we get

`x=3`

Therefore, the value of x is 3.