Example 10.23: Graphing $y = \log_{\frac{1}{3}} x$

Example 10.22: Graphing $y = \log_2 x$

Try It 10.43: Graphing $y = \log_3 x$

Try It 10.44: Graphing $y = \log_5 x$

Try It 10.45: Graphing $y = \log_{\frac{1}{2}} x$

As a trainee in a data analytics upskilling program, you need to manually plot a logarithmic growth model to better understand its behavior. After converting the logarithmic function into its equivalent exponential form, what is the recommended approach for generating the ordered pairs to graph the function?

As an Acoustics Technician measuring sound intensity levels, you are working with a model represented by the logarithmic function $y = \log_2 x$. To create a graph of this relationship using the most efficient manual method, arrange the following steps in the correct procedural order.

A logistics coordinator is plotting a supply chain efficiency model represented by the function $y = \log_5 x$. To generate points for the graph most efficiently after converting the equation to the exponential form $x = 5^y$, the coordinator should select arbitrary values for $x$ and then calculate the corresponding $y$ values.

Converting Logarithmic Models for Graphing

An environmental analyst is plotting a model of carbon sequestration over time using the logarithmic function $y = \log_a x$. To prepare a manual graph for a quarterly report, the analyst must follow a specific sequence of algebraic and procedural steps. Match each component of this graphing process with its correct mathematical form or description.

A medical assistant is graphing the concentration of a therapeutic drug in a patient's bloodstream over time using the logarithmic model $y = \log_3 x$. To manually plot the data points easily, the assistant converts the logarithmic equation into its equivalent ____, which is $x = 3^y$, making it much simpler to select arbitrary values for $y$ and solve for $x$.

Graphing a Logarithmic Growth Projection