SOLUTION: This is the original equation: x=2^-(y-2) What I have to apply to it is the following: Transform the expression into the equivalent logarithmic equation; and evaluate the l

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: This is the original equation: x=2^-(y-2) What I have to apply to it is the following: Transform the expression into the equivalent logarithmic equation; and evaluate the l      Log On


   

Question 270839: This is the original equation:
x=2^-(y-2)
What I have to apply to it is the following: Transform the expression into the equivalent logarithmic equation; and 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.
I think the resulting equivalent logarithmic expression is:
log_2 (x) = -(y-2)
Am I correct? And if I am, how to go about solving this to put it in graphing form? Do I have to solve using the inverse? Any help/advice is appreciated. I really want to understand! Thanks!
Answer by jsmallt9(3759) About Me  (Show Source):
You can put this solution on YOUR website!
log%282%2C+%28x%29%29+=+-%28y-2%29 is correct so far. But there two more things to do. First of all, we should solve for y. So we'll multiply both sides by -1:
-log%282%2C+%28x%29%29+=+y-2
and then add 2 to each side:
2-log%282%2C+%28x%29%29+=+y
The second action is to change the base of the logarithm (unless you have a calculator that can find base 2 logarithms!?). Using the base conversion formala, log%28a%2C+%28p%29%29+=+log%28b%2C+%28p%29%29%2Flog%28b%2C+%28a%29%29, to change the base 2 logarithm into a logarithm your calculator can calculate (base 10 or base e (ln) usually). I'll change to base 10:
2-log%28%28x%29%29%2Flog%28%282%29%29+=+y
Since the instructions say to show your work and I believe the work should show you using the logarithmic equation, this is the equation that should be used for the rest of the problem.

As for the evaluation of this equation with the various values of x, I'll leave that up to you. Just choose a value for x and use your calculator on the left side of the equation to find the y value for that x. Repeat this for all the various x values. This will give you at total of 7 pairs of coordinates to plot on the graph.
Here's what your graph should look like when you are finished. (Note: The graph may look like it touches the y-axis. It does not. The y-axis is a vertical asymptote for this graph. Algebra.com's graphing feature is not perfect.)
graph%28400%2C+400%2C+-2%2C+6%2C+-4%2C+4%2C+2-log%282%2C+x%29%29