Question

section 1.8: logarithmic functions (hor
score: 40/120 answered: 4/12
question 5
write the following as a single logarithm. assume all variables are
\\( \log_{5}(4) + 5\log_{5}(c) = \\) \\(
the answer format in lowercase characters is: log_base (number)
spaces in the answer are optional.
question help: video
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Explanation:

Step1: Apply Power Rule of Logarithms

The power rule states that \( n\log_b(a)=\log_b(a^n) \). For \( 5\log_5(c) \), we apply this rule: \( 5\log_5(c)=\log_5(c^5) \).

Step2: Apply Product Rule of Logarithms

The product rule states that \( \log_b(a)+\log_b(c)=\log_b(ac) \). Now we have \( \log_5(4)+\log_5(c^5) \), so applying the product rule gives \( \log_5(4\times c^5)=\log_5(4c^5) \).

Answer:

\( \log_5(4c^5) \)