Answer
$x=\frac{4}{7}$
Work Step by Step
$12^{2x-1}=(\sqrt[4] {12})^{x}$
This can be written as
$12^{2x-1}=(12^{1/4})^{x}$
Using the property $(a^{m})^{n}=a^{mn}$, we get
$12^{2x-1}=12^{\frac{x}{4}}$
Equating the exponents, we have
$2x-1=\frac{x}{4}$
Multiply both sides by $4$ to get
$4(2x-1)=x$
$\implies 8x-4=x$
Subtracting $x$ from both sides, we have
$7x-4=0$
Adding $4$ to both sides, we obtain
$7x=4$
Divide by $7$ on both sides to have
$x=\frac{4}{7}$
