Using the Change-of-Base Formula with a Calculator

Evaluate $\log_{2} (10)$ using the change-of-base formula with a calculator.

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
According to the change-of-base formula, we can rewrite the log base 2 as a logarithm of any other base. Since our calculators can evaluate the natural log, we might choose to use the natural logarithm, which is the log base $e .$

$\begin{array}{l} \log_{2} 10 = \frac{\ln 10}{\ln 2} & Apply the change of base formula using base e . \\ \approx 3.3219 & Use a calculator to evaluate to 4 decimal places . \end{array}$

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Evaluate $\log_{5} (100)$ using the change-of-base formula.

How did it go?