Question

Use the Change-of-Base Formula and a calculator to evaluate the logarithm. Round your answer to three decimal places.

Answer 1

In order to solve this problem, we need to change the base of the logarithm function so we can use the calculator to solve it. One possible way to do it is by writing it in base 10.

We have:

$\log _ba=\frac{\log _{10}a}{\log _{10}b}$

In this problem, we have:

a = 47

b = 8.1

So, we can write

$\log _{8.1}47=\frac{\log _{10}47}{\log _{10}8.1}$

Now, using a calculator, we obtain:

$\frac{\log_{10}47}{\log_{10}8.1}\cong1.841$

Therefore, the last option is correct.