Question

question
condense the logarithm
\\( q log b + 3 log k \\)

Explanation:

Step1: Apply power rule of logarithms

The power rule of logarithms states that \( n\log_a M=\log_a M^n \). So we can rewrite \( q\log b \) as \( \log b^q \) and \( 3\log k \) as \( \log k^3 \).
\[ q\log b=\log b^q, \quad 3\log k = \log k^3 \]

Step2: Apply product rule of logarithms

The product rule of logarithms states that \( \log_a M+\log_a N=\log_a(MN) \). Now we have \( \log b^q+\log k^3 \), applying the product rule we get:
\[ \log b^q+\log k^3=\log(b^q\cdot k^3) \]

Answer:

\(\log(b^q k^3)\)