Question

Use a calculator to evaluate each expression.

Round your answer to three decimal places.

${\log }_{3}21$

Short answer

The value of ${\log }_{3}21$is 2.771

Step-by-step solution

Step 1. Given Information

Given Expression${\log }_{3}21$

We have to evaluate expression by using a calculator.

Step 2. Solution

For easier calculation on the calculator the base should be b = e

( i.e. we should have the natural logarithm )

Therefore, we will use the change of base formula:

${\log }_{a}M=\frac{{\log }_{b}M}{{\log }_{b}a}$

In our case ${\log }_{a}M=\frac{{\log }_{e}M}{{\log }_{r}a}=\frac{\ln M}{Ina}---\left(1\right)$

So we have${\log }_{3}21=\frac{\ln 21}{\ln 3}=2.771$