Question

Find the value of x if 5^2 ×5^x-5 =625​

Answer 1

Given:

`5^2* 5^(x-5)=625`

To find:

The value of x.

Solution:

We have,

`5^2* 5^(x-5)=625`

It can be written as

`5^2* 5^(x-5)=5* 5* 5* 5`

Using property of exponents, we get

`5^(2+x-5)=5^4`
`[\because a^m* a^n=a^(m+n)]`

`5^(x-3)=5^4`

Comparing the exponents on both sides, we get

`x-3=4`

Adding 3 on both sides, we get

`x=4+3`

`x=7`

Therefore, the value of x is 7.