Evaluate the logarithm using the change-of-base formula. Round your result to three decimal places. $$\log _ { 4 } 6$$
A) $5.292$
B) $1.292$
C) $2.292$
D) $4.292$
E) $3.292$

Question

Evaluate the logarithm using the change-of-base formula. Round your result to three decimal places. $$\log _ { 4 } 6$$ 
A) $5.292$
B) $1.292$
C) $2.292$
D) $4.292$
E) $3.292$

Quizplus · Accepted Answer

The change-of-base formula allows us to rewrite the logarithm in terms of logarithms with a base of our choice, commonly 10 or e. Using base 10, we have $\log_4 6 = \frac{\log_{10} 6}{\log_{10} 4}$. Calculating this gives approximately 1.292.

Evaluate the Logarithm Using the Change-Of-Base Formula log⁡46\log _ { 4 } 6log4​6

Evaluate the Logarithm Using the Change-Of-Base Formula $\log _ { 4 } 6$