SOLUTION: Evaluate the logarithmic equation for three values of x that are greater than 1, three values of x that are between 0 and 1, and at x=1. Show your work. Use the resulting ordered p

Question 251254: Evaluate the logarithmic equation for three values of x that are greater than 1, three values of x that are between 0 and 1, and at x=1. Show your work. Use the resulting ordered pairs to plot the graph; submit the graph via the Dropbox. State the equation of the line asymptotic to the graph (if any).
y = log4 (x) + 4

Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!

Since the logarithm is base 4 ans since no calculator I know can find base 4 logarithms, it will help tremendously if we choose our x values wisely. We want to choose x's that are powers of 4! For the three x's greater than 1: 4, 16 and 64 (since , and ). For the x's between 0 an 1: 1/4, 1/16 and 1/64 (since , and . And even x = 1 is a power of 4 since !

Using these x's we get:
x = 4:
x = 16:
x = 64:
x = 1/4:
x = 1/16:
x = 1/64:
x = 1:
We now have 7 points to plot.

The asymptotes for a logarithmic equation will be vertical asymptotes at values for x that make an argument of a logarithm zero, if any. We have just one logarithm so we find the asymptotes, if any, by setting the argument equal to zero and solving:
x = 0
(Not much solving to do here!) There is a vertical asymptote at x = 0 (aka the y-axis).
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