13) what value is equivalent to \\(\\log_{2} 13\\) to the nearest thousandth? (5 points)\\n\\(\\bigcirc\\)…

13) what value is equivalent to \\(\\log_{2} 13\\) to the nearest thousandth? (5 points)\\n\\(\\bigcirc\\) 0.557\\n\\(\\bigcirc\\) 3.700\\n\\(\\bigcirc\\) 0.270\\n\\(\\bigcirc\\) 0.813

13) what value is equivalent to \\(\\log_{2} 13\\) to the nearest thousandth? (5 points)\\n\\(\\bigcirc\\) 0.557\\n\\(\\bigcirc\\) 3.700\\n\\(\\bigcirc\\) 0.270\\n\\(\\bigcirc\\) 0.813

Answer

Explanation:

Step1: Apply change of base formula

$\log_{2}13 = \frac{\log_{10}13}{\log_{10}2}$

Step2: Calculate log values

$\log_{10}13 \approx 1.1139$, $\log_{10}2 \approx 0.3010$

Step3: Compute the quotient

$\frac{1.1139}{0.3010} \approx 3.700$

Answer:

3.700