Q 27. - Precalculus Enhanced with Graphing Utilities

Question

Find the exact value of the logarithm without using a calculator. 

${\log }_5\left(25\right)$

Step-by-Step Solution

Answer

The exact value of the logarithm is 2.

Step 1. Given information

A logarithmic function is given as ${\log }_5\left(25\right)$.

Step 2. Formula Used

The logarithmic function $y={\log }_a\left(x\right)$ can be changed into an exponential statement as $x=a^y$.

Step 3. Finding Value of the logarithm

Consider ${\log }_5\left(25\right)=x$

By changing rule of logarithm to exponential function,

$$\begin{gathered} 5^x=25 \\ {5}^x=5^2 \\ x=2 \\ {\log }_5\left(25\right)=2 \end{gathered}$$

The required value is,

${\log }_5\left(25\right)=2$