Question

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

${\log }_{\sqrt{3}}16$

Short answer

The value of${\log }_{\sqrt{3}}16$ is$8.328$

Step-by-step solution

Step 1. Given data  

The given logarithm expression is${\log }_{\sqrt{3}}16$

Step 2. Apply change of base formula of the logarithm

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

role="math" localid="1645034870326" ${\log }_{\sqrt{3}}16=\frac{\log 16}{\log \sqrt{3}}$

Step 3. calculation

Enter the expression in the calculator

$\frac{\log 16}{\log \sqrt{3}}=8.328$