Question

Solve for x:

`16^(2x - 1) = 8^(x + 2)`

Answer 1

Given expression is `16^(2x - 1) = 8^(x + 2)`.

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

Thus, `16^(2x - 1) = 8^(x + 2)`

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

`(2)^((8x - 4)) = (2)^((3x + 6))`   ...[∴ (aⁿ)^m = a^nm]

Equating the powers with same bases.

8x – 4 = 3x + 6

8x – 3x = 6 + 4

5x = 10

`x = 10/5`

x = 2

Therefore, the value of x in the given expression is 2.