Question 270839
{{{log(2, (x)) = -(y-2)}}} 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(2, (x)) = y-2}}}
and then add 2 to each side:
{{{2-log(2, (x)) = 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(a, (p)) = log(b, (p))/log(b, (a))}}}, 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((x))/log((2)) = 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.<br>
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(400, 400, -2, 6, -4, 4, 2-log(2, x))}}}