Answer:
x = 0, 1.333333...
Step-by-step explanation:
1) Convert both sides to the same base.
[tex]16^{1.5x^{2} } =16^{2x}[/tex]
2) Cancel the base of 16 on both sides.
[tex]1.5x^{2} =2x[/tex]
3) Move all terms to one side.
[tex]1.5x^{2} -2x=0[/tex]
4) Factor out the common term x.
[tex]x(1.5x-2)=0[/tex]
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...
