Evaluate the given logarithm using the change of base formula and a calculator. Use the natural log.
$\(\log\)_841$

• A. 1.61
• B. 0.9
• C. 0.56
• D. 1.79

Answer: (D)

Verified step by step guidance

1. Understand the change of base formula for logarithms: \( \log_b a = \frac{\log_c a}{\log_c b} \), where \( c \) is a new base, often chosen as 10 or \( e \) (natural log).
2. Choose the natural logarithm (ln) as the new base for calculation. This means you will use \( \ln \) for both the numerator and the denominator in the change of base formula.
3. Apply the change of base formula: \( \log_{841} 8 = \frac{\ln 8}{\ln 841} \).
4. Use a calculator to find \( \ln 8 \) and \( \ln 841 \). Input these values into the formula: \( \frac{\ln 8}{\ln 841} \).
5. Evaluate the expression \( \frac{\ln 8}{\ln 841} \) using the calculator to find the approximate value of the logarithm.