Question

Find the value of x:

`3^2(7^0 + 4^(3x)) = 9 9/16`

Answer 1

Given expression is `3^2(7^0 + 4^(3x)) = 9 9/16`.

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

Thus, `3^2(7^0 + 4^(3x)) = 9 9/16`

`9(1 + 4^(3x)) = 9 + 9/16`

`9(1 + 4^(3x)) = 9(1 + 1/16)`

Divide 9 on both sides.

`1 + 4^(3x) = 1 + 1/16`

By cancelling same terms on both sides, we have

`4^(3x) = 1/16`

4^3x = 4^–2

Equating the powers with same bases.

3x = –2

`x = (-2)/3`

Therefore, the value of x in the given expression is `(-2)/3`.