Got 4 answers for logarithm question but calculator only gives 2

Logarithm question is $\log_9(\sqrt[3]{(x^2-1)^2}) = \frac{1}{3}$

When I solved the question I rewrote the question as $\sqrt[3]{9} = \sqrt[3]{(x^2-1)^2}$, canceled the cube roots and then took the square root of both sides to get $x^2-1 = \pm3$ and then getting $x^2 = 4, x^2 = -2$, giving the solutions of $2, -2, \sqrt{2}i, -\sqrt{2}i,$ however after putting the question into online calculators like wolfram alpha, they only gave the solutions of $2, -2.$

Many calculators only know how to calculate real solutions. When I typed your formula into Wolfram Alpha (using cbrt to indicate cube root) it said:

assuming "cbrt" is the real-valued root

I selected the option to "Use the principal root instead" and it gave me all four answers as expected.

At first, I thought it had to do with $\log$ operating on real numbers; however, this is not correct because even if $x$ is complex, $x^2-1$ is $3$ when $x=2,-2$ and $-3$ when $x=i\sqrt2,-i\sqrt2$ so $(x^2-1)^2$ is always $9$ so the value under the cube root is always real anyway and so there is a real root to $\log$.

So, I think the issue is just with the calculator itself. I don't know how you typed it into Wolfram Alpha, but I got an option to use the principal root and it made the two complex solutions appear as well.