Question

Solve for x:

`36^(x + 1) = 6 xx (216)^(x - 1)`

Answer 1

Given expression is `36^(x + 1) = 6 xx (216)^(x - 1)`.

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

Thus, `36^(x + 1) = 6 xx (216)^(x - 1)`

`(6^2)^(x + 1) = 6 xx (6^3)^(x - 1)`

`(6)^(2(x + 1)) = 6 xx (6)^(3(x - 1))`  ...[∴ (aⁿ)^m = a^nm]

`(6)^(2x + 2) = 6 xx (6)^(3x - 3)`

`(6)^(2x + 2) = (6)^(3x - 3 + 1)`  ...[∴ aⁿ × a^m = a^{n + m}]

`(6)^(2x + 2) = (6)^(3x - 2)`

Equating the powers with same bases.

2x + 2 = 3x – 2

2 + 2 = 3x – 2x

4 = x

Therefore, the value of x in given expression is 4.