Question

Compare the expressions by approximating their values on a calculator. Which two expressions appear to be equivalent.

Answer 1

From the logarithm quotient rule

$\log (\frac{x}{y})=\log x-\log y$

we can see that

$\log (\frac{6}{5})=\log 6-\log 5$

Therefore, expressions a and b are equivalent.

We can corroborate this result because:

$\begin{gathered} \log (\frac{6}{5})=0.07918 \\ \log 6-\log 5=0.7781-0.6989=0.07925 \\ \text{and} \\ \frac{\log 6}{\log 5}=\frac{0.7781}{0.6989}=1.1132 \end{gathered}$