Find the logarithm using the change-of-base formula.
-$\log _ { 24 } 27.46$
A) $1.4387$
B) $1.0424$
C) $0.9593$
D) $1.1442$

Question

Quizplus · Accepted Answer

The change-of-base formula allows us to convert the given logarithm into a form that can be easily calculated using a standard calculator. The formula is $\log_b a = \frac{\log_c a}{\log_c b}$, where $c$ can be any positive value different from 1. Using the common logarithm (base 10) for simplicity, we get $\log_{24} 27.46 = \frac{\log_{10} 27.46}{\log_{10} 24}$. Calculating this gives approximately $1.0424$, which matches option B.

Find the Logarithm Using the Change-Of-Base Formula log⁡2427.46\log _ { 24 } 27.46log24​27.46

Find the Logarithm Using the Change-Of-Base Formula $\log _ { 24 } 27.46$