Question
Log4 2.1 to the nearest thousandth
Answers
GPT-4o mini
To log base 2 of 1.1 (logâ‚‚(1.1)), you can use the change of base formula:
\[
\log_{2}(1.1) = \frac{\log_{10}(1.1)}{\log_{10}(2)}
\]
Calculating those values using logarithm tables or a calculator:
\(\log_{10}(1.1) \approx 0.0414\)
\(\log_{10}(2) \approx 0.3010\)
Now, plugging in the values:
\[
\log_{2}(1.1) \approx \frac{0.0414}{0.3010} \approx 0.137
\]
So, log base 2 of 1.1 rounded to the nearest thousandth is approximately **0.137**.
\[
\log_{2}(1.1) = \frac{\log_{10}(1.1)}{\log_{10}(2)}
\]
Calculating those values using logarithm tables or a calculator:
\(\log_{10}(1.1) \approx 0.0414\)
\(\log_{10}(2) \approx 0.3010\)
Now, plugging in the values:
\[
\log_{2}(1.1) \approx \frac{0.0414}{0.3010} \approx 0.137
\]
So, log base 2 of 1.1 rounded to the nearest thousandth is approximately **0.137**.