Answer
$x=\sqrt 2,-\sqrt 2,0$
Work Step by Step
Re-write the given equation as: $(3^2)^x=3^{x^3}$
or, $3^{2x}=3^{x^3}$
Use the rule power rule: $a^p=a^q$ .
We can see that the base $a=3$ is the same on both sides of the equation.
So, the exponents will also be equal.
This implies that $p=q$
Therefore, $ x^3=2x \\ x^3-2x=0 \\ x(x^2-2) =0 \\x(x+\sqrt 2)(x-\sqrt 2)=0 $
By the zero property rule, we have: $x=\sqrt 2,-\sqrt 2,0$
