Question

Describe the relationship between $y=3^x$ and $y={\log }_{3}x$

Short answer

$y=3^x$ and $y={\log }_{3}x$ are inverse functions of each other.

Step-by-step solution

Step 1. Given Information.

The relationship between the functions $y=3^x$ and $y={\log }_{3}x$ is to be determined.

Step 2. Explanation.

The function $y=3^x$is an exponential function.

The logarithmic equivalent of this exponential function is:

$\begin{array}{l}y=3^x\\ x={\log }_{3}y\end{array}$

This equation looks similar to $y={\log }_{3}x$ except that the variables are interchanged.

This occurs only in inverse of a function.

Step 3. Conclusion.

Hence, the functions $y=3^x$ and $y={\log }_{3}x$ are inverse functions of each other.