Question

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

Answer 1

Answer:

x = 0, 1.333333...

Step-by-step 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...