Which of the following is equivalent to (1)/(log_(3)(m)) ? Choose 1 answer: (A) log_(m)(3) (B) log_(3)(m) (C) -log_(m)(3) (D) -log_(3)(m)

Recognize relationship between reciprocal and change of base: Recognize the relationship between the reciprocal of a logarithm and the change of base formula. The reciprocal of a logarithm can be expressed using the change of base formula. The change of base formula states that log_b(a) = log_c(a) / log_c(b), where b and c are bases and a is the argument of the logarithm.Apply change of base formula: Apply the change of base formula to the given expression. We have (1)/(log_(3)(m)). According to the change of base formula, this can be rewritten as log_m(3) because log_m(3) = log_3(3) / log_3(m) = 1 / log_3(m).Match result with given options: Match the result with the given options. The expression log_m(3) matches with option (A) log_(m)(3).

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Which of the following is equivalent to
(1)/(log_(3)(m)) ?
Choose 1 answer:
(A)
log_(m)(3)
(B)
log_(3)(m)
(C)
-log_(m)(3)
(D)
-log_(3)(m)

Which of the following is equivalent to $\frac{1}{\log _{3}(m)}$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $\log _{m}(3)$ $\newline$ (B) $\log _{3}(m)$ $\newline$ (C) $-\log _{m}(3)$ $\newline$ (D) $-\log _{3}(m)$

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Math Problems

Algebra 2

Product property of logarithms

Full solution

Q. Which of the following is equivalent to

\frac{1}{\log _{3}(m)}

\newline

Choose

1

answer:

\newline

(A)

\log _{m}(3)

\newline

(B)

\log _{3}(m)

\newline

(C)

-\log _{m}(3)

\newline

(D)

-\log _{3}(m)

Recognize relationship between reciprocal and change of base: Recognize the relationship between the reciprocal of a logarithm and the change of base formula. $\newline$ The reciprocal of a logarithm can be expressed using the change of base formula. The change of base formula states that $\log_b(a) = \frac{\log_c(a)}{\log_c(b)}$ , where $b$ and $c$ are bases and $a$ is the argument of the logarithm.
Apply change of base formula: Apply the change of base formula to the given expression. $\newline$ We have $(1)/(\log_{3}(m))$ . According to the change of base formula, this can be rewritten as $\log_m(3)$ because $\log_m(3) = \frac{\log_3(3)}{\log_3(m)} = \frac{1}{\log_3(m)}$ .
Match result with given options: Match the result with the given options. $\newline$ The expression $\log_m(3)$ matches with option (A) $\log_{m}(3)$ .