Question

log3 (5*6^4) how do i expand it if the exponent is inside the parentheses?

Answer 1

log(A*B) = log(A) + log(B)
log(p^q) = q * log(p)

Answer 2

?

Answer 3

\[
\log_3(5*6^4) = \log_3(5) + \log_3(6^4) = \log_3(5) + 4\log_3(6) =
\log_3(5) + 4\log_3(3*2) = \\
\log_3(5) + 4\{\log_3(3) + \log_3(2)\} =
\log_3(5) + 4\{1 + \log_3(2)\} = 4 + 4\log_3(2) + \log_3(5)
\]