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Chapter 7: Problem 8

a. Rewrite each equation in exponential form. b. Use a table of coordinates and the exponential form from part (a) to graph each logarithmic function. Begin by selecting \(-2,-1,0,1\), and 2 for \(y\). \(y=\log _{5} x\)

Short Answer

Expert verified
The equation in exponential form is \(5^y=x\). A table of coordinates and a graph can be created using selected values for \(y\): \(-2,-1,0,1\), and 2.

Step by step solution

01

Rewrite the equation

Starting with \(y=\log _{5} x\). By definition, this equation in exponential form is \(5^y=x\).
02

Create the table of values

Next, create a table by substituting the values \(-2,-1,0,1\), and 2 for \(y\) into the equation \(5^y=x\) to get the corresponding \(x\) values.
03

Graph the logarithmic function

After the \(x\) and \(y\) values have been found, plot these points on a graph and draw a smooth curve through them to represent the logarithmic function \(y=\log _{5} x\). Be aware of the undefined value for y = -1 to indicate the asymptote of the logarithmic function.

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