Question

which of the following is equivalent to \\(\frac{1}{\log_{3}(m)}\\)?
choose 1 answer:
a \\(\log_{m}(3)\\)
b \\(\log_{3}(m)\\)
c \\(-\log_{m}(3)\\)
d \\(-\log_{3}(m)\\)

Explanation:

Step1: Apply change of base formula

Recall that $\log_b(a) = \frac{\ln(a)}{\ln(b)}$, so $\log_3(m) = \frac{\ln(m)}{\ln(3)}$

Step2: Take reciprocal of the expression

$\frac{1}{\log_3(m)} = \frac{1}{\frac{\ln(m)}{\ln(3)}} = \frac{\ln(3)}{\ln(m)}$

Step3: Convert back to log form

$\frac{\ln(3)}{\ln(m)} = \log_m(3)$

Answer:

A. $\log_{m}(3)$