Question

Rounding to three decimal places, approximate ${\log }_{4}73$.

Short answer

The approximate answer is $3.095$

Step-by-step solution

Step 1. Given Information 

We are given an expression ${\log }_{4}73$.

We have to approximate the expression.

Step 2. Approximating

Using change of base formula of logarithm

${\log }_{a}M=\frac{{\log }_{b}M}{{\log }_{b}a}$, we get

$$\begin{gathered} {\log }_{4}73=\frac{{\log }_{10}73}{{\log }_{10}4} \\ {\log }_{4}73=3.095 \end{gathered}$$