Q 26. - Precalculus Enhanced with Graphing Utilities

Question

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

${\log }_8\left(8\right)$

Step-by-Step Solution

Answer

The exact value of the logarithm is 1.

Step 1. Given information

A logarithmic function is given as ${\log }_8\left(8\right)$.

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 ${\log }_8\left(8\right)=x$

By changing rule of logarithm to exponential function,

$$\begin{gathered} 8^x=8 \\ {8}^x=8^1 \\ x=1 \\ {\log }_8\left(8\right)=1 \end{gathered}$$

The required vaue is,

${\log }_8\left(8\right)=1$