Answer
$9$
Work Step by Step
Note that $\sqrt{7} = 7^{\frac{1}{2}}$.
Write $\sqrt{7}$ as $7^{\frac{1}{2}}$ to obtain:
$7^{\frac{x-2}{6}}=7^{\frac{1}{2}}$
Use the rule $a^m=a^n \longrightarrow m=n$ to obtain:
$\dfrac{x-2}{6} = \dfrac{1}{2}$
Cross-multiply to obtain:
$2(x-2) = 6(1)
\\2x-12=6$
Add 12 on both sides of the equation to obtain:
$2x=18$
Divide 2 on both sides of the equation to obtain:
$x = 9$
