Q 25. - Precalculus Enhanced with Graphing Utilities

Question

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

${\log }_2\left(1\right)$

Step-by-Step Solution

Answer

The exact value of the logarithm is 0.

Step 1. Given information

A logarithmic function is given as ${\log }_2\left(1\right)$.

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

The logarithm is ${\log }_2\left(1\right)$.

Consider ${\log }_{2}1=x$

By changing rule,

$$\begin{gathered} 2^x=1 \\ {2}^x=2^0 \\ x=0 \\ {\log }_2\left(1\right)=0 \end{gathered}$$

The required vaue is,

${\log }_2\left(1\right)=0$