Question
Evaluate
log3 32 =
log3 32 =
Answers
GPT-4o mini
To evaluate \( \log_3 32 \), we can use the change of base formula:
\[
\log_b a = \frac{\log_k a}{\log_k b}
\]
where \( k \) can be any positive number. A common choice for \( k \) is 10 or \( e \). Here, we'll choose base 10:
\[
\log_3 32 = \frac{\log_{10} 32}{\log_{10} 3}
\]
Now we can calculate \( \log_{10} 32 \) and \( \log_{10} 3 \) using a calculator:
- \( \log_{10} 32 \approx 1.50515 \)
- \( \log_{10} 3 \approx 0.47712 \)
Substituting these values back into our equation gives:
\[
\log_3 32 \approx \frac{1.50515}{0.47712} \approx 3.15
\]
Thus, the value of \( \log_3 32 \) is approximately \( 3.15 \).
\[
\log_b a = \frac{\log_k a}{\log_k b}
\]
where \( k \) can be any positive number. A common choice for \( k \) is 10 or \( e \). Here, we'll choose base 10:
\[
\log_3 32 = \frac{\log_{10} 32}{\log_{10} 3}
\]
Now we can calculate \( \log_{10} 32 \) and \( \log_{10} 3 \) using a calculator:
- \( \log_{10} 32 \approx 1.50515 \)
- \( \log_{10} 3 \approx 0.47712 \)
Substituting these values back into our equation gives:
\[
\log_3 32 \approx \frac{1.50515}{0.47712} \approx 3.15
\]
Thus, the value of \( \log_3 32 \) is approximately \( 3.15 \).