Use the change of base formula to identify the expression that is equivalent to $\log _ { 5 } 3$ .
A) $\frac { \log 3 } { \log 5 }$
B) $\frac { \log 5 } { \log 3 }$
C) $\frac { \ln 5 } { \ln 3 }$
D) $5 \log 3$

Question

Quizplus · Accepted Answer

The change of base formula allows you to change the base of a logarithm to another base. It is given by $\log_b a = \frac{\log_c a}{\log_c b}$, where $c$ can be any positive value different from 1. Using this formula, $\log_5 3$ can be rewritten as $\frac{\log 3}{\log 5}$ or $\frac{\ln 3}{\ln 5}$, but only the first option is provided, making A the correct choice.

Use the Change of Base Formula to Identify the Expression log⁡53\log _ { 5 } 3log5​3

Use the Change of Base Formula to Identify the Expression $\log _ { 5 } 3$