Question

In the following exercises, rounding to three decimal places, approximate each logarithm.

${\log }_{5}97$

Short answer

The value of${\log }_{5}97$is $2.842$

Step-by-step solution

Step 1. Given data  

The given logarithm expression is${\log }_{5}97$

Step 2. Apply change of base formula of the logarithm

Use change of base formula of the logarithm ${\log }_a\left(m\right)=\frac{{\log }_b\left(m\right)}{{\log }_b\left(a\right)}$

${\log }_{5}97=\frac{\log 97}{\log 5}$

Step 3. calculation

Enter the expression in the calculator

$\frac{\log 97}{\log 5}=2.842$