Question

What is the logarithm of 3.85 [base 2]

Answer 1

To calculate the logarithm of \( 3.85 \) with base \( 2 \), you can use the change of base formula, which states that:

\[
\log_b(a) = \frac{\log_c(a)}{\log_c(b)}
\]

where \( c \) can be any positive real number (commonly base 10 or base \( e \)). Using base 10 for this example:

\[
\log_2(3.85) = \frac{\log_{10}(3.85)}{\log_{10}(2)}
\]

Using a calculator:

1. Calculate \( \log_{10}(3.85) \) which is approximately \( 0.585 \).
2. Calculate \( \log_{10}(2) \), which is approximately \( 0.301 \).

Now substitute these values into the formula:

\[
\log_2(3.85) \approx \frac{0.585}{0.301} \approx 1.943
\]

Therefore,

\[
\log_2(3.85) \approx 1.943
\]