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

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> 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      Log On


   

Question 283758: 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. State the equation of the line asymptotic to the graph (if any).
y= log[5]x
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
As a base 5 logarithm, the only values for y you will be able to find will those for x's that are known powers of 5. 1 is a power of 5. It is 5%5E0. For x's greater than 1 use 5, 25 and 125 (which are powers of 5 should know (or be able to figure out). For x's between 0 and 1 use 1/5, 1/25 and 1/125. But these values will not make the graph easy. It will be hard to graph x values of 25 and 125 on the same graph as x values of 1/25 and 1/125 unless you have an immense piece of graph paper.

A more practical approach would be to use the base conversion formula, log%28a%2C+%28p%29%29+=+log%28b%2C+%28p%29%29%2Flog%28b%2C+%28a%29%29, to rewrite the base 5 logarithm as an equivalent expression of base 10 logarithms:
y+=+log%28%28x%29%29%2Flog%28%285%29%29
Now we can pick any (positive) numbers we want for x and use our calculator to find the value for y. I'll leave that up to you to do.

For the asymptote, logarithmic functions have a vertical asymptote for the value of x that makes the argument 0. It works like this because arguments of logarithms cannot be zero or negative. So zero represents the highest invalid argument. X must have values that result in arguments greater than zero.

Your argument is simply x so x=0 (i.e. the y-axis) is a vertical asymptote for the graph of your function.