Use the following approximations to find the approximate value of the logarithmic expression:
$\log _ { b } 3 \approx 0.5 \quad \log _ { b } 8 \approx 0.9$
$\log _ { b } 5 \approx 0.7 \quad \log _ { b } 20 \approx 1.3$
-$\log _ { b } \sqrt [ 3 ] { 8 }$ (Round answer to nearest hundredth.)
A) $0.45$
B) $2.7$
C) $0.3$
D) 2

Question

Use the following approximations to find the approximate value of the logarithmic expression: 
$\log _ { b } 3 \approx 0.5 \quad \log _ { b } 8 \approx 0.9$
$\log _ { b } 5 \approx 0.7 \quad \log _ { b } 20 \approx 1.3$
-$\log _ { b } \sqrt [ 3 ] { 8 }$ (Round answer to nearest hundredth.)
A) $0.45$
B) $2.7$
C) $0.3$
D) 2

Quizplus · Accepted Answer

The expression $\log_b \sqrt[3]{8}$ can be simplified to $\frac{1}{3} \log_b 8$, since $\sqrt[3]{8} = 8^{1/3}$. Given $\log_b 8 \approx 0.9$, the value is $\frac{1}{3} \times 0.9 = 0.3$.

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