Use the following approximations to find the approximate value of the logarithmic expression: $\log _ { b } 3 \approx 0.5$ logb $8 \approx 0.9$
$\log _ { b } 5 \approx 0.7$ logb $20 \approx 1.3$
-$\log _ { \mathrm { b } } 125$
A) $0.343$
B) $0.23$
C) $2.1$
D) $3.7$

Question

Quizplus · Accepted Answer

Given $\log_b 125$, we can rewrite 125 as $5^3$. Thus, $\log_b 125 = \log_b (5^3) = 3 \log_b 5$. Using the given approximation $\log_b 5 \approx 0.7$, we find $3 \log_b 5 \approx 3 \times 0.7 = 2.1$.

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