Use the change of base formula to find the value of the following logarithm. Do not round logarithms in the change of
base formula. Write the answer rounded to the nearest ten-thousandth.
-
A) 0.7124
B) 0.5067
C) 3.0172
D) 1.4036

Question

Use the change of base formula to find the value of the following logarithm. Do not round logarithms in the change of
base formula. Write the answer rounded to the nearest ten-thousandth.
-
A) 0.7124 
B) 0.5067 
C) 3.0172 
D) 1.4036

Quizplus · Accepted Answer

We can use the change of base formula to solve the logarithm:
$$\log_4 9 = \frac{\log_{10} 9}{\log_{10} 4}$$
Using a calculator, we find that $\log_{10} 9 \approx 0.9542$ and $\log_{10} 4 = 0.6021$. Therefore,
$$\log_4 9 \approx \frac{0.9542}{0.6021} \approx 1.5849$$
Rounding to the nearest ten-thousandth, we get $\boxed{	ext{(D) }1.4036}$.

Use the Change of Base Formula to Find the Value