Question

Solve the equation (2^2x +2) (2^3x -7)= 2^25

Answer 1

`\Huge \boxed{x=6}`

`\rule[225]{225}{2}`

Explanation:

`(2^(2x +2)) (2^(3x -7))= 2^(25)`

When multiplying same bases, add the exponents.

`(2^(2x +2+3x -7))= 2^(25)`

`(2^(5x -5))= 2^(25)`

Cancelling the same bases from both sides.

`5x-5=25`

Adding 5 to both sides.

`5x=30`

Dividing both sides by 5.

`x=6`

`\rule[225]{225}{2}`