Chapter 10: Q2. (page 535)

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

Short Answer

Expert verified

$y = 3^{x}$ 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.

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

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Explanation.

Step 3. Conclusion.

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Describe the relationship between y=3x and y=log3x

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Explanation.

Step 3. Conclusion.

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