Question

How would you solve this equation:

`9^(a-8)+7=74`

Answer 1

`a=(\ln \left(67\right))/(2\ln \left(3\right))+8`

`a = (log 67)/(2log3) +8`

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=(\ln \left(67\right))/(2\ln \left(3\right))+8`

Step 2:

`9^(a-8)+7=74\\`