Answer it all for Brainliest Once Alice discovers that log10 162 means “the power to which I should raise 10 to get 162,” she grows curious about what the graph of a logarithmic function looks like. She realizes there is a different logarithmic function for each base. For example, one such function is defined by the equation y = log2 x.

Alice’s investigations rely heavily on the fact that the equation c = loga b means the same thing as the equation ac = b. This relationship allows her to work with exponential equations, with which she is more comfortable.

1. For each equation, choose values for x for which you can easily compute the value of y. Plot the resulting points. Choose enough points that you can sketch the graph accurately.

a. y = log2 x

b. y = log3 x

2. Graph the equation y = log10 x on your calculator.

3. Compare the graph of the logarithmic function using base 2 with the graphs of logarithmic functions using other bases. In general, how does the graph change as the base increases? Why?

4. How does the graph of a logarithmic function compare with the graph of the corresponding exponential function?