Approximate the logarithm to four decimal places using the change of base formula.
-$\log _ { 4 } 2$
A) $2.0000$
B) $- 0.3010$
C) $0.9031$
D) $0.5000$

Question

Quizplus · Accepted Answer

The change of base formula is $\log_b a = \frac{\log_c a}{\log_c b}$. Using base 10 (common logarithm) for simplicity, we get $\log_4 2 = \frac{\log 2}{\log 4}$. Since $\log 2 \approx 0.3010$ and $\log 4 = \log (2^2) = 2\log 2 \approx 0.6020$, the division gives approximately $0.5$, making the correct answer $0.5000$.

Approximate the Logarithm to Four Decimal Places Using the Change log⁡42\log _ { 4 } 2log4​2

Approximate the Logarithm to Four Decimal Places Using the Change $\log _ { 4 } 2$