CPM Homework Help : CCA2 Problem 6-115

Use the definition of a logarithm to change $\log_27$ into a logarithmic expression of base 5.

Step 1:

Start with the definition of the logarithm.
$\log_27=x\\2^x=7$

Step 2:

Take the log base 5 of both sides.
$\log_5(2^x)=\log_57$

Step 3:

Use the Power Property of Logarithms.
$x(\log_52)=\log_57$

Answer:

$\log_{2}7 =\frac{\log_{5}7}{\log_{5}2}$

Notice that this answer shows a very quick way to change bases.