Question

Solve for x 64^x^2 = 256^x

Answer 1

x = 0, 1.333333...

Explanation:

1) Convert both sides to the same base.

`16^{1.5x^(2) } =16^(2x)`

2) Cancel the base of 16 on both sides.

`1.5x^(2) =2x`

3) Move all terms to one side.

`1.5x^(2) -2x=0`

4) Factor out the common term x.

`x(1.5x-2)=0`

5) Solve for x.

1 - Ask: When will x(1.5x-2) equal zero?

When x = 0 or 1.5x - 2 = 0
2 - Solve each of the 2 equations above.

x = 0, 1.333333...