Use the change of base formula to complete the fraction.(2 points)

log5(37)=?/?

1 answer

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.