Question

log7 90 in form log m/log n

Answer 1

To express \(\log_7 90\) in the form \(\frac{\log m}{\log n}\), we can use the change of base formula for logarithms. The change of base formula states:

\[
\log_b a = \frac{\log_k a}{\log_k b}
\]

where \(k\) is any positive number (usually 10 or \(e\) are used, but you can use any base).

Using this formula, we can convert \(\log_7 90\) as follows:

\[
\log_7 90 = \frac{\log 90}{\log 7}
\]

Here, we can choose any base for the logarithm (commonly base 10 or the natural logarithm base \(e\)), but it is customary to simply write it as \(\log\) when the base is not specified.

Thus, we have expressed \(\log_7 90\) in the desired form:

\[
\log_7 90 = \frac{\log 90}{\log 7}
\]

In summary:

\[
\log_7 90 = \frac{\log m}{\log n} \text{ with } m = 90 \text{ and } n = 7
\]