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How can a table of values be created in order to graph a logarithmic function? (1 point) Plug in only even \( y \)-values to the logarithmic equation to find corresponding odd \( x \)-values. Rewrite the logarithm in exponential form and plug in the \( y \)-values. Plug in \( y \)-values to the logarithmic equation to find the corresponding \( x \)-values. Rewrite the logarithm in exponential form and plug in the \( x \)-values.

Ask by Horton Hall. in the United States
Feb 04,2025

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To create a table of values for a logarithmic function, plug in \( y \)-values into the equation to find the corresponding \( x \)-values.

Solución

To create a table of values for graphing a logarithmic function, the correct approach is: **Plug in \( y \)-values to the logarithmic equation to find the corresponding \( x \)-values.** Here's why this method is appropriate: 1. **Understanding Logarithmic Functions**: A logarithmic function can be expressed in the form \( y = \log_b(x) \), where \( b \) is the base of the logarithm. This means that for a given \( y \)-value, you can find the corresponding \( x \)-value by rearranging the equation. 2. **Finding Corresponding Values**: By selecting specific \( y \)-values (for example, \( y = 0, 1, 2, \ldots \)), you can calculate the corresponding \( x \)-values using the equation \( x = b^y \). This allows you to create pairs of \( (x, y) \) that can be plotted on a graph. 3. **Example**: If you choose \( y = 0, 1, 2 \) and your logarithm is base 10, you would calculate: - For \( y = 0 \): \( x = 10^0 = 1 \) - For \( y = 1 \): \( x = 10^1 = 10 \) - For \( y = 2 \): \( x = 10^2 = 100 \) This results in the points \( (1, 0), (10, 1), (100, 2) \), which can be plotted to graph the logarithmic function. Thus, the correct answer is to **plug in \( y \)-values to the logarithmic equation to find the corresponding \( x \)-values**.

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Bonus Knowledge

To create a table of values for a logarithmic function, start by plugging in a range of \( y \)-values into the logarithmic equation, which will help you find the corresponding \( x \)-values. For instance, if you're working with the function \( y = \log_b(x) \), determine \( x \) by calculating \( x = b^y \) for different \( y \) values such as -2, -1, 0, 1, and 2. Additionally, when you create your table, consider the properties of logarithmic functions: they are only defined for positive \( x \)-values. Common mistakes include attempting to use negative or zero values for \( x \), which would lead to undefined logarithms. Keep in mind that logarithms can have a slow growth, so spacing your \( y \)-values adequately will keep your graph looking nice and smooth!

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