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)

Isolate exponential part: First, let's isolate the exponential part by dividing both sides by 4. 2^(-(t)/(5)) = 288 / 4 2^(-(t)/(5)) = 72Solve for t: Now, we need to solve for t. To do this, we can take the logarithm with base 2 of both sides. -(t)/(5) = log_(2)(72)Multiply by -5: Multiply both sides by -5 to solve for t. t = -5 * log_(2)(72)Match answer choices: Now we look at the answer choices to see which one matches our result. (A) t=-5log_(8)(288) - Incorrect, wrong base and number inside the log. (B) t=-5log_(288)(8) - Incorrect, the log is written backwards. (C) t=-5log_(2)(72) - Correct, matches our result. (D) t=-5log_(72)(2) - Incorrect, the log is written backwards.

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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)

$4 \cdot 2^{-\frac{t}{5}}=288$ $\newline$ Which of the following is the solution of the equation? $\newline$ Choose $1$ answer: $\newline$ (A) $t=-5 \log _{8}(288)$ $\newline$ (B) $t=-5 \log _{288}(8)$ $\newline$ (C) $t=-5 \log _{2}(72)$ $\newline$ (D) $t=-5 \log _{72}(2)$

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Math Problems

Algebra 1

Compare linear and exponential growth

Full solution

4 \cdot 2^{-\frac{t}{5}}=288

\newline

Which of the following is the solution of the equation?

\newline

Choose

1

answer:

\newline

(A)

t=-5 \log _{8}(288)

\newline

(B)

t=-5 \log _{288}(8)

\newline

(C)

t=-5 \log _{2}(72)

\newline

(D)

t=-5 \log _{72}(2)

Isolate exponential part: First, let's isolate the exponential part by dividing both sides by $4$ . $\newline$ $2^{-(t)/(5)} = 288 / 4$ $\newline$ $2^{-(t)/(5)} = 72$
Solve for $t$ : Now, we need to solve for $t$ . To do this, we can take the logarithm with base $2$ of both sides. $\newline$ $-\frac{t}{5} = \log_{2}(72)$
Multiply by $-5$ : Multiply both sides by $-5$ to solve for $t$ . $t = -5 \times \log_{2}(72)$
Match answer choices: Now we look at the answer choices to see which one matches our result. $\newline$ (A) $t=-5\log_{8}(288)$ - Incorrect, wrong base and number inside the log. $\newline$ (B) $t=-5\log_{288}(8)$ - Incorrect, the log is written backwards. $\newline$ (C) $t=-5\log_{2}(72)$ - Correct, matches our result. $\newline$ (D) $t=-5\log_{72}(2)$ - Incorrect, the log is written backwards.