Question:
If \(\log_{10}3=0.4771,\ \log_{10}7=0.8450\), then the value of \(\log_3 7\) is
If \(\log_{10}3=0.4771,\ \log_{10}7=0.8450\), then the value of \(\log_3 7\) is
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To convert a logarithm from one base to another, divide both logarithms using any convenient common base such as 10 or \(e\).
Updated On: Jun 9, 2026
- 1.771
- 1.5710
- 1.8460
- 1.6842
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The Correct Option is A
Solution and Explanation
Concept:
When the logarithms are given in a different base, we use the Change of Base Formula:
\[
\log_a b=\frac{\log_c b}{\log_c a}
\]
Here, logarithms to base 10 are provided.
Step 1: Apply the change of base formula.
\[ \log_3 7 = \frac{\log_{10}7}{\log_{10}3} \] Substituting the given values: \[ \log_3 7 = \frac{0.8450}{0.4771} \]
Step 2: Perform the division.
\[ \frac{0.8450}{0.4771} \approx 1.771 \] Therefore, \[ \log_3 7 \approx 1.771 \] 1.771
Step 1: Apply the change of base formula.
\[ \log_3 7 = \frac{\log_{10}7}{\log_{10}3} \] Substituting the given values: \[ \log_3 7 = \frac{0.8450}{0.4771} \]
Step 2: Perform the division.
\[ \frac{0.8450}{0.4771} \approx 1.771 \] Therefore, \[ \log_3 7 \approx 1.771 \] 1.771
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