Answer:
[tex]a=\frac{\ln \left(67\right)}{2\ln \left(3\right)}+8[/tex]
[tex]a = \frac{log 67}{2log3} +8[/tex]
Step-by-step explanation:
[tex]9^{a-8} +7=74 \\\\\mathrm{Subtract\:}7\mathrm{\:from\:both\:sides}\\\\9^{a-8}+7-7=74-7\\\\Simplify\\9^{a-8}=67[/tex]
Apply exponents rules
[tex]\left(a-8\right)\ln \left(9\right)=\ln \left(67\right)\\\\Solve \\\\a=\frac{\ln \left(67\right)}{2\ln \left(3\right)}+8[/tex]
Step 2:
[tex]9^{a-8}+7=74\\[/tex]
