4*5^(-6t)=2000 Which of the following is the solution of the equation? Choose 1 answer: (A) t=(-log_(5)(500))/(6) (B) t=(-log_(20)(2000))/(6) (c) t=(-log_(2000)(20))/(6) (D) t=(-log_(500)(5))/(6)

Divide and isolate variable term: Divide both sides of the equation by 4 to isolate the term with the variable t. Calculation: $ \frac{4 \cdot 5^{-6t}}{4} = \frac{2000}{4} $ $ 5^{-6t} = 500 $Apply logarithm to both sides: Apply the logarithm to both sides of the equation to solve for t. Calculation: $ \log(5^{-6t}) = \log(500) $Use logarithm property: Use the property of logarithms that allows us to bring the exponent in front of the logarithm. Calculation: $ -6t \cdot \log(5) = \log(500) $Divide by -6log(5): Divide both sides of the equation by $-6 \log(5)$ to solve for t. Calculation: $ t = \frac{\log(500)}{-6 \log(5)} $Correct previous error: Recognize that $\log(500)$ can be simplified to $\log(5^3)$ since $500 = 5^3$. Calculation: $ t = \frac{\log(5^3)}{-6 \log(5)} $Apply the property of logarithms that allows us to bring the exponent out in front of the logarithm. Calculation: $ t = \frac{3 \log(5)}{-6 \log(5)} $Simplify the expression by canceling out $\log(5)$ on the numerator and the denominator. Calculation: $ t = \frac{3}{-6} $Simplify the fraction to find the value of t. Calculation: $ t = -\frac{1}{2} $Realize that a mistake was made in the previous steps because the simplification of $\log(500)$ to $\log(5^3)$ was incorrect since $500$ is not equal to $5^3$. Therefore, we need to correct the error and go back to Step 4.

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4*5^(-6t)=2000
Which of the following is the solution of the equation?
Choose 1 answer:
(A)
t=(-log_(5)(500))/(6)
(B)
t=(-log_(20)(2000))/(6)
(c)
t=(-log_(2000)(20))/(6)
(D)
t=(-log_(500)(5))/(6)

$4 \cdot 5^{-6 t}=2000$ $\newline$ Which of the following is the solution of the equation? $\newline$ Choose $1$ answer: $\newline$ (A) $t=\frac{-\log _{5}(500)}{6}$ $\newline$ (B) $t=\frac{-\log _{20}(2000)}{6}$ $\newline$ (C) $t=\frac{-\log _{2000}(20)}{6}$ $\newline$ (D) $t=\frac{-\log _{500}(5)}{6}$

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Math Problems

Algebra 2

Product property of logarithms

Full solution

4 \cdot 5^{-6 t}=2000

\newline

Which of the following is the solution of the equation?

\newline

Choose

1

answer:

\newline

(A)

t=\frac{-\log _{5}(500)}{6}

\newline

(B)

t=\frac{-\log _{20}(2000)}{6}

\newline

(C)

t=\frac{-\log _{2000}(20)}{6}

\newline

(D)

t=\frac{-\log _{500}(5)}{6}

Divide and isolate variable term: Divide both sides of the equation by $4$ to isolate the term with the variable t. $\newline$ Calculation: $\frac{4 \cdot 5^{-6t}}{4} = \frac{2000}{4}$ $\newline$ $5^{-6t} = 500$
Apply logarithm to both sides: Apply the logarithm to both sides of the equation to solve for t. $\newline$ Calculation: $\log(5^{-6t}) = \log(500)$
Use logarithm property: Use the property of logarithms that allows us to bring the exponent in front of the logarithm. $\newline$ Calculation: $-6t \cdot \log(5) = \log(500)$
Divide by $-6$ log( $5$ ): Divide both sides of the equation by $-6 \log(5)$ to solve for t. $\newline$ Calculation: $t = \frac{\log(500)}{-6 \log(5)}$
Correct previous error: Recognize that $\log(500)$ can be simplified to $\log(5^3)$ since $500 = 5^3$ . $\newline$ Calculation: $t = \frac{\log(5^3)}{-6 \log(5)}$
Correct previous error: Recognize that $\log(500)$ can be simplified to $\log(5^3)$ since $500 = 5^3$ . $\newline$ Calculation: $t = \frac{\log(5^3)}{-6 \log(5)}$ Apply the property of logarithms that allows us to bring the exponent out in front of the logarithm. $\newline$ Calculation: $t = \frac{3 \log(5)}{-6 \log(5)}$
Correct previous error: Recognize that $\log(500)$ can be simplified to $\log(5^3)$ since $500 = 5^3$ . $\newline$ Calculation: $t = \frac{\log(5^3)}{-6 \log(5)}$ Apply the property of logarithms that allows us to bring the exponent out in front of the logarithm. $\newline$ Calculation: $t = \frac{3 \log(5)}{-6 \log(5)}$ Simplify the expression by canceling out $\log(5)$ on the numerator and the denominator. $\newline$ Calculation: $t = \frac{3}{-6}$
Correct previous error: Recognize that $\log(500)$ can be simplified to $\log(5^3)$ since $500 = 5^3$ . $\newline$ Calculation: $t = \frac{\log(5^3)}{-6 \log(5)}$ Apply the property of logarithms that allows us to bring the exponent out in front of the logarithm. $\newline$ Calculation: $t = \frac{3 \log(5)}{-6 \log(5)}$ Simplify the expression by canceling out $\log(5)$ on the numerator and the denominator. $\newline$ Calculation: $t = \frac{3}{-6}$ Simplify the fraction to find the value of t. $\newline$ Calculation: $t = -\frac{1}{2}$
Correct previous error: Recognize that $\log(500)$ can be simplified to $\log(5^3)$ since $500 = 5^3$ . $\newline$ Calculation: $t = \frac{\log(5^3)}{-6 \log(5)}$ Apply the property of logarithms that allows us to bring the exponent out in front of the logarithm. $\newline$ Calculation: $t = \frac{3 \log(5)}{-6 \log(5)}$ Simplify the expression by canceling out $\log(5)$ on the numerator and the denominator. $\newline$ Calculation: $t = \frac{3}{-6}$ Simplify the fraction to find the value of t. $\newline$ Calculation: $t = -\frac{1}{2}$ Realize that a mistake was made in the previous steps because the simplification of $\log(500)$ to $\log(5^3)$ was incorrect since $\log(5^3)$ $0$ is not equal to $\log(5^3)$ $1$ . Therefore, we need to correct the error and go back to Step $4$ .