Question

how would you solve this equation:
$9^{a-8}+7=74$

Answer 1

Answer:

$a=\frac{\ln \left(67\right)}{2\ln \left(3\right)}+8$

$a = \frac{log 67}{2log3} +8$

Step-by-step explanation:

$9^{a-8} +7=74 \\\\\mathrm{Subtract\:}7\mathrm{\:from\:both\:sides}\\\\9^{a-8}+7-7=74-7\\\\Simplify\\9^{a-8}=67$

Apply exponents rules

$\left(a-8\right)\ln \left(9\right)=\ln \left(67\right)\\\\Solve \\\\a=\frac{\ln \left(67\right)}{2\ln \left(3\right)}+8$

Step 2:

$9^{a-8}+7=74$