solve: $6^{2x - 3}=6^{-2x + 1}$\n$x=-1$\n$x = 0$\n$x = 1$\n$x = 4$\ndone

Explanation:

Step1: Use exponential - equality property

Since the bases are the same ($a^m=a^n$ implies $m = n$ for $a>0,a\neq1$), for $6^{2x - 3}=6^{-2x + 1}$, we have $2x-3=-2x + 1$.

Step2: Add $2x$ to both sides

$2x-3+2x=-2x + 1+2x$, which simplifies to $4x-3=1$.

Step3: Add 3 to both sides

$4x-3 + 3=1+3$, so $4x=4$.

Step4: Divide both sides by 4

$\frac{4x}{4}=\frac{4}{4}$, then $x = 1$.

Answer:

$x = 1$