Question

solve the logarithmic equation. write the answer in exact, simplified form. \\(\log_{6}(y - 1) = 2\\) the solution set is \\(\square\\).

Explanation:

Step1: Convert log to exponential form

Recall that if $\log_b(a) = c$, then $b^c = a$. For $\log_6(y - 1) = 2$, we have $6^2 = y - 1$.

Step2: Calculate $6^2$ and solve for y

$6^2 = 36$, so the equation becomes $36 = y - 1$. Add 1 to both sides: $y = 36 + 1 = 37$.

Answer:

$\{37\}$