## Intermediate Algebra for College Students (7th Edition)

$5$
Note that $\sqrt{6} = 6^{\frac{1}{2}}$. Write $\sqrt{6}$ as $6^{\frac{1}{2}}$ to obtain: $6^{\frac{x-3}{4}}=6^{\frac{1}{2}}$ Use the rule $a^m=a^n \longrightarrow m=n$ to obtain: $\dfrac{x-3}{4} = \dfrac{1}{2}$ Cross-multiply to obtain: $2(x-3) = 4(1) \\2x-6=4$ Add 6 on both sides of the equation to obtain: $2x=10$ Divide 2 on both sides of the equation to obtain: $x = 5$