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.
-$$\log _ { 4 } 0.069$$
A)-4.6446
B)0.0415
C)-0.5185
D)-1.9286

Question

Quizplus · Accepted Answer

The change of base formula is $\log_b a = \frac{\log_c a}{\log_c b}$. Using base 10, $\log_4 0.069 = \frac{\log_{10} 0.069}{\log_{10} 4}$. Calculating this gives approximately -1.9286.

Use the Change of Base Formula to Find the Value log⁡40.069\log _ { 4 } 0.069log4​0.069

Use the Change of Base Formula to Find the Value $\log _ { 4 } 0.069$