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 term: Isolate the exponential term. To solve for t, we first need to isolate the term with the variable t in the exponent. We do this by dividing both sides of the equation by 8. 8 * 5^((-t)/9) = 346 (8 * 5^((-t)/9)) / 8 = 346 / 8 5^((-t)/9) = 43.25Apply logarithm: Apply the logarithm to both sides of the equation. To solve for the exponent, we can apply the logarithm with base 5 to both sides of the equation. This will allow us to remove the exponent on the left side. log_5(5^((-t)/9)) = log_5(43.25)Use property of logarithms: Use the property of logarithms that log_b(b^x) = x. By applying this property, we can simplify the left side of the equation to just the exponent. (-t)/9 = log_5(43.25)Solve for t: Solve for t. To solve for t, we need to multiply both sides of the equation by -9. (-t)/9 * (-9) = log_5(43.25) * (-9) 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

Algebra 1

Multiplication with rational exponents

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 term: Isolate the exponential term. $\newline$ To solve for $t$ , we first need to isolate the term with the variable $t$ in the exponent. We do this by dividing both sides of the equation by $8$ . $\newline$ $8 \times 5^{(-t)/9} = 346$ $\newline$ $(8 \times 5^{(-t)/9}) / 8 = 346 / 8$ $\newline$ $5^{(-t)/9} = 43.25$
Apply logarithm: Apply the logarithm to both sides of the equation. $\newline$ To solve for the exponent, we can apply the logarithm with base $5$ to both sides of the equation. This will allow us to remove the exponent on the left side. $\newline$ $\log_5(5^{(-t)/9}) = \log_5(43.25)$
Use property of logarithms: Use the property of logarithms that $\log_b(b^x) = x$ . By applying this property, we can simplify the left side of the equation to just the exponent. $\frac{-t}{9} = \log_5(43.25)$
Solve for t: Solve for t. $\newline$ To solve for t, we need to multiply both sides of the equation by -9＂).$\newline\$\frac{-t}{9} \times (-9) = \log_5(43.25) \times (-9)$$\newline$$t = -9 \times \log_5(43.25)$