Question

use common logarithms or natural logarithms and a calculator to evaluate the following.
log_{12} 89.5
evaluate the expression.
log_{12} 89.5 approx square
(type an integer or a decimal. do not round until the final answer. then round to four decimal places as needed.)

Explanation:

Step1: Recall the change of base formula

The change of base formula for logarithms is $\log_b a=\frac{\log a}{\log b}$ (or $\frac{\ln a}{\ln b}$). For $\log_{12} 89.5$, we can use this formula. Let's use common logarithms (base 10). So we have $\log_{12} 89.5 = \frac{\log 89.5}{\log 12}$.

Step2: Calculate the numerator and denominator

Using a calculator, $\log 89.5\approx1.9518$, and $\log 12\approx1.0792$.

Step3: Divide the two values

Now, divide the numerator by the denominator: $\frac{1.9518}{1.0792}\approx1.8086$.

Answer:

1.8086