Question
Use the change of base formula to complete the fraction.(2 points)
log5(37)=?/?
log5(37)=?/?
Answers
GPT-4o mini
To use the change of base formula for logarithms, you can convert \(\log_5(37)\) to a base that is often more convenient, such as base 10 or base \(e\). The change of base formula is given by:
\[
\log_b(a) = \frac{\log_k(a)}{\log_k(b)}
\]
where \(b\) is the base of the original logarithm, \(a\) is the argument, and \(k\) is the new base.
Using base 10, we have:
\[
\log_5(37) = \frac{\log_{10}(37)}{\log_{10}(5)}
\]
In this case, \(\log_{10}(37)\) and \(\log_{10}(5)\) are typically calculated using a calculator.
The fraction representation would therefore be:
\[
\log_5(37) = \frac{\log(37)}{\log(5)}
\]
Thus, filling in the values for the fraction \(\log_5(37) = ?/?\), we can state:
\[
\log_5(37) = \frac{\log(37)}{\log(5)}
\]
So, the answer is:
\[
\log_5(37) = \frac{\log(37)}{\log(5)}
\]
If you need specific numerical values for \(\log(37)\) and \(\log(5)\), you can evaluate them with a calculator to obtain a numerical approximation, but the fraction can remain in that form as a representation.
\[
\log_b(a) = \frac{\log_k(a)}{\log_k(b)}
\]
where \(b\) is the base of the original logarithm, \(a\) is the argument, and \(k\) is the new base.
Using base 10, we have:
\[
\log_5(37) = \frac{\log_{10}(37)}{\log_{10}(5)}
\]
In this case, \(\log_{10}(37)\) and \(\log_{10}(5)\) are typically calculated using a calculator.
The fraction representation would therefore be:
\[
\log_5(37) = \frac{\log(37)}{\log(5)}
\]
Thus, filling in the values for the fraction \(\log_5(37) = ?/?\), we can state:
\[
\log_5(37) = \frac{\log(37)}{\log(5)}
\]
So, the answer is:
\[
\log_5(37) = \frac{\log(37)}{\log(5)}
\]
If you need specific numerical values for \(\log(37)\) and \(\log(5)\), you can evaluate them with a calculator to obtain a numerical approximation, but the fraction can remain in that form as a representation.