Chapter 4, Problem 22RE

To determine

To Express: The equation ${\log }_{6}37=x$ in exponential form

Answer to Problem 22RE

  $6^x=37$

Explanation of Solution

Given: ${\log }_{6}37=x$

FORMULA USED:

  $\begin{array}{l}{\log }_{a}x=y\\ a^y=x\end{array}$

Since $6$ is a positive number with $6\ne 1$ .

So,

The definition of the logarithm function with base $6$ implies that

  $\begin{array}{l}{\log }_{6}37=x\\ 6^x=37\end{array}$

Hence, the exponential form of the given expression is $6^x=37$