8*5^((-t)/(9))=346 Which of the following is the solution of the equation? Choose 1 answer: (A) t=9log_(5)(43.25) (B) t=-9log_(40)(346) (c) t=-9log_(5)(43.25) (D) t=9log_(346)(40)

Isolate exponential part: First, let's isolate the exponential part by dividing both sides by 8. 8 * 5^((-t)/(9)) = 346 5^((-t)/(9)) = 346 / 8 5^((-t)/(9)) = 43.25Take logarithm with base 5: Now, we'll take the logarithm with base 5 of both sides to solve for t. log_5(5^((-t)/(9))) = log_5(43.25)Apply logarithm property: Using the property of logarithms, the exponent on the left side comes down in front. ((-t)/(9)) * log_5(5) = log_5(43.25)Simplify left side: Since log_5(5) is 1, we can simplify the left side. -t/9 = log_5(43.25)Multiply both sides: Now, we multiply both sides by -9 to solve for t. t = -9 * log_5(43.25)

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8*5^((-t)/(9))=346
Which of the following is the solution of the equation?
Choose 1 answer:
(A)
t=9log_(5)(43.25)
(B)
t=-9log_(40)(346)
(c)
t=-9log_(5)(43.25)
(D)
t=9log_(346)(40)

$8 \cdot 5^{\frac{-t}{9}}=346$ $\newline$ Which of the following is the solution of the equation? $\newline$ Choose $1$ answer: $\newline$ (A) $t=9 \log _{5}(43.25)$ $\newline$ (B) $t=-9 \log _{40}(346)$ $\newline$ (C) $t=-9 \log _{5}(43.25)$ $\newline$ (D) $t=9 \log _{346}(40)$

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Math Problems

Grade 6

Multiply two decimals: where does the decimal point go?

Full solution

8 \cdot 5^{\frac{-t}{9}}=346

\newline

Which of the following is the solution of the equation?

\newline

Choose

1

answer:

\newline

(A)

t=9 \log _{5}(43.25)

\newline

(B)

t=-9 \log _{40}(346)

\newline

(C)

t=-9 \log _{5}(43.25)

\newline

(D)

t=9 \log _{346}(40)

Isolate exponential part: First, let's isolate the exponential part by dividing both sides by $8$ . $\newline$ $8 \times 5^{(-t)/(9)} = 346$ $\newline$ $5^{(-t)/(9)} = 346 / 8$ $\newline$ $5^{(-t)/(9)} = 43.25$
Take logarithm with base $5$ : Now, we'll take the logarithm with base $5$ of both sides to solve for $t$ . $\log_5(5^{(-\frac{t}{9})}) = \log_5(43.25)$
Apply logarithm property: Using the property of logarithms, the exponent on the left side comes down in front. $\left(\frac{-t}{9}\right) \cdot \log_5(5) = \log_5(43.25)$
Simplify left side: Since $\log_5(5)$ is $1$ , we can simplify the left side. $\newline$ $-\frac{t}{9} = \log_5(43.25)$
Multiply both sides: Now, we multiply both sides by $-9$ to solve for $t$ . $t = -9 \times \log_5(43.25)$