Answer
$x=5$
Work Step by Step
RECALL:
(i) If $a^M=a^N$, then $M=N.$
(ii) $\sqrt[n]{a}=a^{\frac{1}{n}}.$
Use rule (ii) above to obtain
$7^{\frac{x-2}{6}}=7^{\frac{1}{2}}.$
Use rule (i) above to obtain
$\dfrac{x-2}{6}=\dfrac{1}{2}.$
Cross-multiply to obtain
$\begin{array}{ccc}
&2(x-2) &= &6(1)
\\&2x-4 &= &6
\\&2x &= &6+4
\\&2x&= &10
\\&x &= &\dfrac{10}{2}
\\&x &= &5
\\\end{array}.$
