Solve for x:
[tex]\begin{gathered} 5^{(x-7)}=8 \\ \end{gathered}[/tex]To find x, we are going to solve the exponent, taking log of both sides:
[tex]\begin{gathered} \log (5^{x-7})=\log (8) \\ x-7\cdot\log (5)=\log (8) \\ x-7=\frac{\log (8)}{\log (5)} \\ x-7=1.292 \\ x=1.292+7 \\ x=8.292 \end{gathered}[/tex]