Answer
$6$
Work Step by Step
Rewrite the equation using the definition of logarithm.
$x^{(4x-24)}=1$
Set the power equal to 0 because $x^0=1$ when $x\ne0$. Also, do not forget that $x\gt0$ and $x\ne1$. If $x$ does not match both of these criteria, the result of $\log_x$ would be undefined.
$4x-24=0$
Simplify.
$x=6$
