Question

write the expression below as a single logarithm in simplest form.\\(\log_{b} 4 + 2\log_{b} 3\\)

Explanation:

Step1: Apply the power rule of logarithms

The power rule states that \( n\log_b M=\log_b M^n \). For \( 2\log_b 3 \), we have \( 2\log_b 3=\log_b 3^2=\log_b 9 \).

Step2: Apply the product rule of logarithms

The product rule states that \( \log_b M+\log_b N = \log_b(MN) \). Now we have \( \log_b 4+\log_b 9 \), so applying the product rule gives \( \log_b(4\times9)=\log_b 36 \).

Answer:

\(\log_{b} 36\)