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Which of the following is equivalent to (log(t))/(log_(8)(t)) ? Choose 1 answer: (A) log(8) (B) log_(8)(t^(2)) (C) (1)/(log(8)) (D) (1)/(log_(8)(t^(2)))

Which of the following is equivalent to log⁡(t)log⁡8(t) \frac{\log (t)}{\log _{8}(t)} ?\newlineChoose 11 answer:\newline(A) log⁡(8) \log (8) \newline(B) log⁡8(t2) \log _{8}\left(t^{2}\right) \newline(C) 1log⁡(8) \frac{1}{\log (8)} \newline(D) 1log⁡8(t2) \frac{1}{\log _{8}\left(t^{2}\right)}

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Full solution

Q. Which of the following is equivalent to log⁡(t)log⁡8(t) \frac{\log (t)}{\log _{8}(t)} ?\newlineChoose 11 answer:\newline(A) log⁡(8) \log (8) \newline(B) log⁡8(t2) \log _{8}\left(t^{2}\right) \newline(C) 1log⁡(8) \frac{1}{\log (8)} \newline(D) 1log⁡8(t2) \frac{1}{\log _{8}\left(t^{2}\right)}
  1. Multiply by log⁡(8)\log(8): Simplify the expression by multiplying both numerator and denominator by log⁡(8)\log(8).log⁡(t)⋅log⁡(8)log⁡(t)log⁡(8)⋅log⁡(8)\frac{\log(t) \cdot \log(8)}{\frac{\log(t)}{\log(8)} \cdot \log(8)}
  2. Cancel out log⁡(t)\log(t): Cancel out log⁡(t)\log(t) in the numerator and denominator.log⁡(8)\log(8)

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