Multiple Choice
Write the single logarithm as a sum or difference of logs.
0. Functions
Properties of Logarithms
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Evaluate the given logarithm using the change of base formula and a calculator. Use the natural log.
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Verified step by step guidance1
Step 1: Recall the change of base formula for logarithms, which states that \( \log_b(a) = \frac{\ln(a)}{\ln(b)} \), where \( \ln \) represents the natural logarithm.
Step 2: Identify the base \( b \) and the argument \( a \) from the given logarithm \( \log_8(41) \). Here, \( b = 8 \) and \( a = 41 \).
Step 3: Apply the change of base formula: \( \log_8(41) = \frac{\ln(41)}{\ln(8)} \).
Step 4: Use a calculator to compute \( \ln(41) \) and \( \ln(8) \) separately. Ensure you input the values correctly into the calculator.
Step 5: Divide the result of \( \ln(41) \) by \( \ln(8) \) to find the value of \( \log_8(41) \).
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