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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 1log⁡3(m) \frac{1}{\log _{3}(m)} ?\newlineChoose 11 answer:\newline(A) log⁡m(3) \log _{m}(3) \newline(B) log⁡3(m) \log _{3}(m) \newline(C) −log⁡m(3) -\log _{m}(3) \newline(D) −log⁡3(m) -\log _{3}(m)

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Full solution

Q. Which of the following is equivalent to 1log⁡3(m) \frac{1}{\log _{3}(m)} ?\newlineChoose 11 answer:\newline(A) log⁡m(3) \log _{m}(3) \newline(B) log⁡3(m) \log _{3}(m) \newline(C) −log⁡m(3) -\log _{m}(3) \newline(D) −log⁡3(m) -\log _{3}(m)
  1. Recognize relationship between reciprocal and change of base: Recognize the relationship between the reciprocal of a logarithm and the change of base formula.\newlineThe 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)\log_b(a) = \frac{\log_c(a)}{\log_c(b)}, where bb and cc are bases and aa is the argument of the logarithm.
  2. Apply change of base formula: Apply the change of base formula to the given expression.\newlineWe have (1)/(log⁡3(m))(1)/(\log_{3}(m)). According to the change of base formula, this can be rewritten as log⁡m(3)\log_m(3) because log⁡m(3)=log⁡3(3)log⁡3(m)=1log⁡3(m)\log_m(3) = \frac{\log_3(3)}{\log_3(m)} = \frac{1}{\log_3(m)}.
  3. Match result with given options: Match the result with the given options.\newlineThe expression log⁡m(3)\log_m(3) matches with option (A) log⁡m(3)\log_{m}(3).

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