Answer
a) $10$; $e$; Change-of-Base; $12; 7; 1.28;$
b) Yes
Work Step by Step
a) Most calculators are able to calculate logarithms with base $10$ and base $e$. In order to find logarithms with other bases, we use the Change-of-Base Formula.
To find $\log_7{12}$ we have:
$$\log_7{12}=\dfrac{\log 12}{\log 7}\approx 1.28.$$
b) Using the natural logarithm leads us to the same result as the Change-of-Base Formula is:
$$\log_b x=\dfrac{\log_a x}{\log_a b},$$
where $b$ is the initial base and $a$ is the new base. The Change-of-Base formula is true for any base $a$, therefore for $e$ also, so natural logarithm can be used to calculate $\log_7 {12}$.
