Use the following approximations to find the approximate value of the logarithmic expression:
$\log _ { b } 3 \approx 0.5 \quad \log _ { b } 8 \approx 0.9$
$\log _ { b } 5 \approx 0.7 \quad \log _ { b } 20 \approx 1.3$
-$\log _ { b } \sqrt { 3 }$ (Round answer to nearest hundredth.)
A) $0.71$
B) 1
C) $0.25$
D) $1.73$

Question

Use the following approximations to find the approximate value of the logarithmic expression: 
$\log _ { b } 3 \approx 0.5 \quad \log _ { b } 8 \approx 0.9$
$\log _ { b } 5 \approx 0.7 \quad \log _ { b } 20 \approx 1.3$
-$\log _ { b } \sqrt { 3 }$ (Round answer to nearest hundredth.)
A) $0.71$
B) 1
C) $0.25$
D) $1.73$

Quizplus · Accepted Answer

The logarithm of the square root of a number is equal to one-half the logarithm of the number itself. Therefore, $\log_b \sqrt{3} = \frac{1}{2} \log_b 3 \approx \frac{1}{2} \times 0.5 = 0.25$.

Use the Following Approximations to Find the Approximate Value of the Logarithmic