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

User Warem
by
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1 Answer

10 votes

Answer:

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...

User Maryssa
by
8.4k points

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