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

log_(2)((1)/(50))~~

Evaluate the logarithm. $\newline$ Round your answer to the nearest thousandth. $\newline$ $\log _{2}\left(\frac{1}{50}\right) \approx$

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Product property of logarithms

Full solution

Q. Evaluate the logarithm.

\newline

Round your answer to the nearest thousandth.

\newline

\log _{2}\left(\frac{1}{50}\right) \approx

Identify Property: Identify the property of logarithm used to evaluate $\log_2(\frac{1}{50})$ . We can use the quotient property of logarithms to separate the numerator and the denominator into two logarithms. Quotient Property: \log_b \left(\frac{P}{Q}\right) = \log_b P - \log_b Q
Apply Quotient Property: Apply the quotient property to \(\log_2(\frac{1}{50}). Using the quotient property, we can write $\log_2(\frac{1}{50})$ as $\log_2(1) - \log_2(50)$ .
Evaluate Logs: Evaluate $\log_2(1)$ and $\log_2(50)$ . We know that $\log_2(1)$ is $0$ because any $\log$ base $b$ of $1$ is $0$ . To evaluate $\log_2(50)$ , we can use a calculator or logarithm tables.
Calculate Log: Calculate $\log_2(50)$ using a calculator. $\newline$ Using a calculator, we find that $\log_2(50)$ is approximately $5.6439$ .
Subtract Logs: Subtract $\log_2(50)$ from $\log_2(1)$ . $\newline$ Now we subtract the values: $0 - 5.6439 = -5.6439$ .
Round Result: Round the result to the nearest thousandth. $\newline$ Rounding $-5.6439$ to the nearest thousandth gives us $-5.644$ .

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