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 $20 \approx 1.3$
-$\log _ { b } 160$
A) $1.17$
B) 28
C) 160
D) $2.2$

Question

Quizplus · Accepted Answer

The expression can be simplified using the properties of logarithms. Given $\log_b 160$, we can express 160 as a product of the numbers provided in the approximations: $160 = 8 \times 20$. Therefore, $\log_b 160 = \log_b (8 \times 20) = \log_b 8 + \log_b 20$. Using the given approximations, $\log_b 8 \approx 0.9$ and $\log_b 20 \approx 1.3$, so $\log_b 160 \approx 0.9 + 1.3 = 2.2$.

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