Chapter 3, Problem 27RE

To determine

To write the below logarithmic equation in exponential form:

  $4^3=64$

Answer to Problem 27RE

  ${\log }_{4}64=3$

Explanation of Solution

Given:

  $4^3=64$

Concept Used:

For $a\in R^{+}\&a\ne 1$ and $u\in R^{+}$ :

• $a^x=u\iff x={\log }_{a}u$

Calculation:

To write the exponential equation

  $4^2=64$

in logarithmic equation use the property $a^x=u\iff x={\log }_{a}u$

As,

  $\begin{array}{c}{4}^3=64\\ \Rightarrow 3={\log }_{4}64\\ \Rightarrow {\log }_{4}64=3\end{array}$

Thus, the given exponential equation can be written in logarithmic equation as:

  ${\log }_{4}64=3$