Question

Simplify, without use of a calculator: \[ 3 \log 3+\log 125 \]

Answer 1

Step 1: Try to write any quantities as exponents 125 can be written as \(5^{3}\).

Step 2: Simplify

\[
\begin{aligned}
3 \log 3+\log 125 &=3 \log 3+\log 5^{3} \\
&=3 \log 3+3 \log 5 \because \log _{a}\left(x^{b}\right)=b \log _{a}(x) \\
&=3 \log 15 \quad(\text { Logarithm Law 3) }
\end{aligned}
\]

Step 3: Final Answer We cannot simplify any further. The final answer is:
\(3 \log 15\)