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4*2^(-(t)/(5))=288 Which of the following is the solution of the equation? Choose 1 answer: (A) t=-5log_(8)(288) (B) t=-5log_(288)(8) (C) t=-5log_(2)(72) (D) t=-5log_(72)(2)

4⋅2−t5=288 4 \cdot 2^{-\frac{t}{5}}=288 \newlineWhich of the following is the solution of the equation?\newlineChoose 11 answer:\newline(A) t=−5log⁡8(288) t=-5 \log _{8}(288) \newline(B) t=−5log⁡288(8) t=-5 \log _{288}(8) \newline(C) t=−5log⁡2(72) t=-5 \log _{2}(72) \newline(D) t=−5log⁡72(2) t=-5 \log _{72}(2)

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Full solution

Q. 4⋅2−t5=288 4 \cdot 2^{-\frac{t}{5}}=288 \newlineWhich of the following is the solution of the equation?\newlineChoose 11 answer:\newline(A) t=−5log⁡8(288) t=-5 \log _{8}(288) \newline(B) t=−5log⁡288(8) t=-5 \log _{288}(8) \newline(C) t=−5log⁡2(72) t=-5 \log _{2}(72) \newline(D) t=−5log⁡72(2) t=-5 \log _{72}(2)
  1. Isolate exponential part: First, let's isolate the exponential part by dividing both sides by 44.\newline2−(t)/(5)=288/42^{-(t)/(5)} = 288 / 4\newline2−(t)/(5)=722^{-(t)/(5)} = 72
  2. Solve for tt: Now, we need to solve for tt. To do this, we can take the logarithm with base 22 of both sides.\newline−t5=log⁡2(72)-\frac{t}{5} = \log_{2}(72)
  3. Multiply by −5-5: Multiply both sides by −5-5 to solve for tt.t=−5×log⁡2(72)t = -5 \times \log_{2}(72)
  4. Match answer choices: Now we look at the answer choices to see which one matches our result.\newline(A) t=−5log⁡8(288)t=-5\log_{8}(288) - Incorrect, wrong base and number inside the log.\newline(B) t=−5log⁡288(8)t=-5\log_{288}(8) - Incorrect, the log is written backwards.\newline(C) t=−5log⁡2(72)t=-5\log_{2}(72) - Correct, matches our result.\newline(D) t=−5log⁡72(2)t=-5\log_{72}(2) - Incorrect, the log is written backwards.

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