Question

Find the value of x:

`5^2(3^0 + 6^(2x)) = 25 25/36`

Answer 1

Given expression is `5^2(3^0 + 6^(2x)) = 25 25/36`.

We need to find the value of x in the given expression.

Thus, `5^2(3^0 + 6^(2x)) = 25 25/36`

`25(1 + 6^(2x)) = 25 + 25/36`

`25(1 + 6^(2x)) = 25(1 + 1/36)`

Divide 25 on both sides.

`1 + 6^(2x) = 1 + 1/36`

By cancelling same terms on both sides, we have

`6^(2x) = 1/36`

6^2x = 6^–2

Equating the powers with same bases.

2x = –2

`x = (-2)/2 = -1`

Therefore, the value of x in the given expression is –1.