Chapter 12.2, Problem 50E

To determine

To calculate:

Value of ${\log }_{11}265$ by using change of base formula.

Answer to Problem 50E

Value of ${\log }_{11}265$ by using change of base formula is $2.33$ .

Explanation of Solution

Given information:

  ${\log }_{11}265$

Calculation:

The formula is,

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

Now substitute the values,

  $\begin{array}{l}{\log }_{n}265=\frac{{\log }_{10}265}{{\log }_{10}11}\\ {\log }_{n}265=\frac{2.42}{1.04}\\ {\log }_{n}265=2.33\end{array}$

Hence, Value of ${\log }_{11}265$ by using change of base formula is $2.33$ .