Answer
a. $\displaystyle \log_{b}x=\frac{\log_{a}x}{\log_{a}b}$
b. $\log_{7}30 \approx$0.57212502854
Work Step by Step
a.
The Change of Base Formula is given on p. 357.
$\displaystyle \log_{b}x=\frac{\log_{a}x}{\log_{a}b}$
b.
$\displaystyle \log_{7}30=\frac{\log_{10}7}{\log_{10}30}\qquad$ common logarithms,
for which we use a calculator
$\displaystyle \approx\frac{0.845098040014}{1.47712125472}\approx$0.57212502854
a. $\displaystyle \log_{b}x=\frac{\log_{a}x}{\log_{a}b}$
b. $\log_{7}30 \approx$0.57212502854
