Question

Solve for x:

`81^(x - 2) = 27^(x + 1)`

Answer 1

Given expression is `81^(x - 2) = 27^(x + 1)`.

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

Thus, `81^(x - 2) = 27^(x + 1)`

`(3^4)^(x - 2) = (3^3)^(x + 1)`

`(3)^(4(x - 2)) = (3)^(3(x + 1))`   ...[∴ (aⁿ)^m = a^nm]

`(3)^(4x - 8) = (3)^(3x + 3)`

Equating the powers with same bases.

4x – 8 = 3x + 3

4x – 3x = 3 + 8

x = 11

Therefore, the value of x in given expression is 11.