Question

the two expressions below have the same value when rounded to the nearest hundredth.

\\(\log_{5} b\\) \\(\log_{9} 48\\)

what is the approximate value of \\(\log b\\) to the nearest hundredth?

\\(\bigcirc\\) 0.93
\\(\bigcirc\\) 1.23
\\(\bigcirc\\) 9.16
\\(\bigcirc\\) 65.53

Explanation:

Evaluate the known logarithmic expression

Using the Logarithmic Evaluation knowledge point

$$ \log_{9} 48 = \frac{\ln 48}{\ln 9} \approx \frac{3.8712}{2.1972} \approx 1.7618 $$

Set up the equation for b

Using the Change of Base Formula knowledge point

$$
LATEXBLOCK0
$$

Calculate the target logarithmic expression

Using the Logarithmic Evaluation knowledge point

$$ \log b = \log_{10} b \approx \log_{10} 17.031 \approx 1.2312 $$

Round to the nearest hundredth

Using the Logarithmic Evaluation knowledge point

$$ \log b \approx 1.23 $$

Answer:

• (A) 0.93
• (B) 1.23 (Correct answer)
• (C) 9.16
• (D) 65.53