SOLUTION: Graph f(x) = (-logbase5*(2x)) -1 Could someone please walk me though each step? I understand that the graph is reflected over the x-axis, and that the whole thing is translated

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Graph f(x) = (-logbase5*(2x)) -1 Could someone please walk me though each step? I understand that the graph is reflected over the x-axis, and that the whole thing is translated       Log On


   



Question 962124: Graph f(x) = (-logbase5*(2x)) -1
Could someone please walk me though each step? I understand that the graph is reflected over the x-axis, and that the whole thing is translated down one unit. However, I don't know how to figure out each point that I need.
Thank you for your help!

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+f%28x%29+=+-log%28+5%2C%28+2x+-+1+%29+%29+
Multiply both sides by +-1+
+-f%28x%29+=+log%28+5%2C%28+2x+-+1+%29+%29+
I can say +y+=+f%28x%29+,
and the inverse of this is:
+2x+-+1+=+5%5E%28-y%29+
The graph doesn't exist when
+2x+-+1+%3C=+0+
+2x+%3C=+1+
+x+%3C=+1%2F2+
----------------
+y+=+0+
+x+=+1+
-----------
+y+=+-1+
+x+=+3+
etc.
-----------
Here's the plot:
+graph%28+500%2C+500%2C+-3%2C+6%2C+-3%2C+6%2C+-log%28+5%2C+%282x-1+%29%29++%29+