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

Question

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

Bytelearn · Accepted Answer

Recognize relationship and formula: Recognize the relationship between the given expression and the change of base formula. The expression (log(3))/(log_(n)(3)) can be related to the change of base formula for logarithms, which states that log_(b)(a) = (log(c)(a))/(log(c)(b)) for any positive a, b, and c, where a and b are not equal to 1.Apply change of base formula: Apply the change of base formula to the given expression. Using the change of base formula, we can rewrite (log(3))/(log_(n)(3)) as log_(n)(3). This is because the expression is essentially asking for the base n logarithm of 3, which is the definition of log_(n)(3).Match with answer choices: Match the rewritten expression with the answer choices. The expression log_(n)(3) matches with choice (B) log_(3)(n) if we consider the properties of logarithms. However, we need to verify this by considering the change of base formula correctly.Correct application of formula: Correct the application of the change of base formula. Upon re-evaluating the previous step, we realize that the change of base formula should be applied as follows: (log(3))/(log_(n)(3)) is equivalent to log_(n)(3) using the base 10 logarithm, which is actually log_(3)(n) according to the change of base formula. Therefore, the correct expression is log_(3)(n), which corresponds to choice (B).

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

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