[color=#0000ff]Since all exponential functions pass the horizontal line test, they are one-to-one functions. As a result, each exponential function has an inverse. These inverse functions are known as logarithmic functions.[br][br][/color][math]y=log_ax[/math][color=#0000ff] if and only if [/color][math]a^y=x[/math][color=#0000ff][br][br]The graph of [/color][math]g\left(x\right)=2^x[/math][color=#0000ff] and the graph of [/color][math]g^{-1}\left(x\right)=log_2x[/math][color=#0000ff] are given in the applet. [/color][br][br][b][color=#ff0000]Explore the Sliders:[/color][/b][br]Use the sliders to adjust the base of the exponential and logarithmic functions.[br]Observe how changing the base affects the shape of both graphs.[br][br][b][color=#ff0000]Input Your Values:[/color][br][/b]In the input boxes, type different values for the exponent or logarithmic arguments. Observe how the graphs update based on your inputs.[br][br][b][color=#ff0000]Compare the Functions:[/color][/b][br]Identify how the graphs of the exponential function and its logarithmic inverse reflect over the line [math]y=x[/math]. Check if each point on the exponential function has a corresponding inverse point on the logarithmic function.[br][br][b][color=#ff0000]Analyze Symmetry:[/color][br][/b]Experiment with different values to see the symmetry between exponential and logarithmic graphs.[br]Try to predict the graph of the logarithmic function based on changes you make to the exponential function.