Question

solve the logarithmic equation. write the answer in exact, simplified form. \\(\log_{8}(a + 9) = 2\\) the solution set is \\(\square\\).

Explanation:

Step1: Convert log to exponential form

Recall that if $\log_{b}(x) = y$, then $b^{y}=x$. For $\log_{8}(a + 9)=2$, we have $b = 8$, $y=2$, and $x=a + 9$. So, $8^{2}=a + 9$.

Step2: Calculate $8^{2}$ and solve for $a$

Calculate $8^{2}=64$. Then the equation becomes $64=a + 9$. Subtract 9 from both sides: $a=64 - 9=55$.

Answer:

$\{55\}$