Exponential equation with absolute value: $9^{|3x-1|}=3^{8x-2}$

Question

$$9^{|3x-1|}=3^{8x-2}$$

Can someone show me the steps on how to solve this, i've been trying for 30 minutes

Answer 1

We have $$\large 9^{|3x -1|} = 3^{(2\cdot|3x - 1|)} = 3^{8x - 2}$$ So we need only solve $$\begin{align}2\cdot |3x - 1| = 8x - 2 & \iff |3x - 1| = 4x - 1\\ \\ & \iff 3x - 1 = 4x - 1 \quad\text{or}\quad-(3x - 1) = 4x - 1\end{align}$$

Answer 2

HINT:

$x^a=x^b \implies a=b$

$|x|=a \implies x= \pm a$.