Answer
$x=5$
Work Step by Step
We are given the exponential equation $6^{\frac{x-3}{4}}=\sqrt6$.
We can express each side using a common base and then solve for $x$.
$6^{\frac{x-3}{4}}=6^{\frac{1}{2}}=\sqrt 6$
Take the natural log of both sides.
$ln(6^{\frac{x-3}{4}})=ln(6^{\frac{1}{2}})$
$(\frac{x-3}{4})ln(6)=\frac{1}{2}ln(6)$
Divide both sides by $ln(6)$.
$\frac{x-3}{4}=\frac{1}{2}$
Multiply both sides by 4.
$x-3=2$
Add 3 to both sides.
$x=5$
