Evaluate the logarithm. Round your answer to the nearest thousandth. 2log_(3)((1)/(52))~~◻

Understand the expression: Understand the logarithm expression. We are given the expression 2log₃(1/52) and need to evaluate it. The base of the logarithm is 3, and the argument is 1/52. The coefficient 2 in front of the logarithm indicates that we need to multiply the logarithm by 2 after evaluating it.Apply logarithm properties: Apply the logarithm properties. We can use the property of logarithms that states logₐ(b^n) = n*logₐ(b). In this case, we can take the coefficient 2 and make it the exponent of the argument inside the logarithm: 2log₃(1/52) = log₃((1/52)^2).Calculate square of fraction: Calculate the square of 1/52. We need to square the fraction 1/52: (1/52)^2 = 1^2 / 52^2 = 1 / 2704. So, our expression becomes log₃(1/2704).Evaluate the logarithm: Evaluate the logarithm. To evaluate log₃(1/2704), we need to find the power to which 3 must be raised to get 1/2704. Since 3 raised to any positive power will not result in a fraction smaller than 1, we know that the power must be negative. However, without a calculator, finding the exact value of this logarithm is not straightforward. We can use a calculator to find the value.Use calculator for evaluation: Use a calculator to find the value of the logarithm. Using a calculator, we find: log₃(1/2704) ≈ -6.287.Round the answer: Round the answer to the nearest thousandth. Rounding -6.287 to the nearest thousandth gives us -6.287 since it is already at the thousandth place.

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Evaluate the logarithm.
Round your answer to the nearest thousandth.

2log_(3)((1)/(52))~~◻

Evaluate the logarithm. $\newline$ Round your answer to the nearest thousandth. $\newline$ $2 \log _{3}\left(\frac{1}{52}\right) \approx \square$

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Algebra 1

Compare linear, exponential, and quadratic growth

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Q. Evaluate the logarithm.

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Round your answer to the nearest thousandth.

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2 \log _{3}\left(\frac{1}{52}\right) \approx \square

Understand the expression: Understand the logarithm expression. $\newline$ We are given the expression $2\log_{3}(\frac{1}{52})$ and need to evaluate it. The base of the logarithm is $3$ , and the argument is $\frac{1}{52}$ . The coefficient $2$ in front of the logarithm indicates that we need to multiply the logarithm by $2$ after evaluating it.
Apply logarithm properties: Apply the logarithm properties. $\newline$ We can use the property of logarithms that states $\log_a(b^n) = n\log_a(b)$ . In this case, we can take the coefficient $2$ and make it the exponent of the argument inside the logarithm: $\newline$ $2\log_3(\frac{1}{52}) = \log_3((\frac{1}{52})^2)$ .
Calculate square of fraction: Calculate the square of $\frac{1}{52}$ . We need to square the fraction $\frac{1}{52}$ : $(\frac{1}{52})^2 = \frac{1^2}{52^2} = \frac{1}{2704}$ . So, our expression becomes $\log_3(\frac{1}{2704})$ .
Evaluate the logarithm: Evaluate the logarithm. $\newline$ To evaluate $\log_3(\frac{1}{2704})$ , we need to find the power to which $3$ must be raised to get $\frac{1}{2704}$ . Since $3$ raised to any positive power will not result in a fraction smaller than $1$ , we know that the power must be negative. However, without a calculator, finding the exact value of this logarithm is not straightforward. We can use a calculator to find the value.
Use calculator for evaluation: Use a calculator to find the value of the logarithm. $\newline$ Using a calculator, we find: $\newline$ $\log_3(\frac{1}{2704}) \approx -6.287$ .
Round the answer: Round the answer to the nearest thousandth. $\newline$ Rounding $-6.287$ to the nearest thousandth gives us $-6.287$ since it is already at the thousandth place.