Question

expand the logarithm fully using the properties of logs. express the final answer in terms of \\(\log x\\). \\(\log 3x^3\\)

Explanation:

Step1: Apply Product Rule of Logs

The product rule of logarithms states that \(\log(ab)=\log a+\log b\). For \(\log 3x^{3}\), we can split it as \(\log 3+\log x^{3}\).

Step2: Apply Power Rule of Logs

The power rule of logarithms states that \(\log a^{n}=n\log a\). For \(\log x^{3}\), applying the power rule gives \(3\log x\). So combining with the previous step, we have \(\log 3 + 3\log x\).

Answer:

\(\log 3 + 3\log x\)