Question

Expand and simplify the following expression. If possible, write your answer without exponents.

log4(.25(x+7)^6)

Answer 1

\[ \log_4(.25(x+7)^6)=\log_40.25+\log_4(x+7)^6\]
\[=\log_4\frac 14+6\log_4(x+7)\]
\[=\log_44^{-1}+6\log(x+7)\]
\[=-1+6\log(x+7)\]

Answer 2

There are so many rules for logs and my brain rejects them. Thank you.