solve $(3x-1)^{x-1}=1$ Q:How do I solve for $x$? $$(3x-1)^{x-1}=1$$
When I first saw this question I thought it was quadratic equation, $(3x-1)(x-1)=1$. But friend say no! It is raised to the power of $x-1$. What?!!
I could take the log
$$(x-1)\log(3x-1)=0$$
$\log(3x-1)=0$
$3x-1=1$
$x=\frac{2}{3}$.
There is a problem, he told me there are more answers!!
I can't sees it. Can anyone please show me if there are more answer?

Hint:$$(x-1)\log(3x-1)=0\implies \begin{array} xx-1=0\\ 3x-1=1\end{array}$$
