Question

which is equivalent to \\(\log_{\frac{1}{2}} 462\\)?

• \\(\frac{\log_{\frac{1}{2}} 462}{\log_{462} \frac{1}{2}}\\)
• \\(\frac{\log 462}{\log \frac{1}{2}}\\)
• \\(\frac{\log \frac{1}{2}}{\log 462}\\)

find the value of \\(\log_{\frac{1}{2}} 462\\) to four decimal places.

• \\(-8.8517\\)
• \\(-0.1130\\)
• \\(0.1130\\)
• \\(8.8517\\)

Explanation:

Apply the change of base formula

Using the Change of Base Formula knowledge point

$$ \log_{a} b = \frac{\log_{c} b}{\log_{c} a} $$

$$ \log_{\frac{1}{2}} 462 = \frac{\log 462}{\log \frac{1}{2}} $$

Evaluate the logarithmic expression

Using the Logarithmic Evaluation knowledge point

$$ \log 462 \approx 2.664637 $$

$$ \log \frac{1}{2} = \log 0.5 \approx -0.301030 $$

$$ \frac{2.664637}{-0.301030} \approx -8.8517 $$

Answer:

Question 1

• (A) \(\frac{\log_{\frac{1}{2}} 462}{\log_{462} \frac{1}{2}}\)
• (B) \(\frac{\log 462}{\log \frac{1}{2}}\) (Correct answer)
• (C) \(\frac{\log \frac{1}{2}}{\log 462}\)

Question 2

• (A) \(-8.8517\) (Correct answer)
• (B) \(-0.1130\)
• (C) \(0.1130\)
• (D) \(8.8517\)