Use a calculator and the change-of-base formula to find the logarithm to four decimal places. $$\log _ { 3 } \pi$$
A)0.6189
B)1.0420
C)1.8074
D)1.0342
E)0.9415

Question

Quizplus · Accepted Answer

The change-of-base formula allows us to convert the given logarithm to a base that our calculator can handle, typically base 10 or base e (natural logarithm). The formula is $\log_b a = \frac{\log_c a}{\log_c b}$, where $c$ can be any positive value, but we commonly use 10 or e for calculators. Using base 10, we get $\log_3 \pi = \frac{\log_{10} \pi}{\log_{10} 3}$. Plugging into a calculator, we find this value to be approximately 1.0420.

Use a Calculator and the Change-Of-Base Formula to Find the Logarithm