SOLUTION: Where does the graph of v(x) = log5 (x) and its inverse intersect? we tried using a graphing calc and it says no solution. we are not very certain if it correct. thank you!

Algebra ->  Graphs -> SOLUTION: Where does the graph of v(x) = log5 (x) and its inverse intersect? we tried using a graphing calc and it says no solution. we are not very certain if it correct. thank you!      Log On


   

Question 1149089: Where does the graph of v(x) = log5 (x) and its inverse intersect?
we tried using a graphing calc and it says no solution. we are not very certain if it correct. thank you!
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!
+f%28x%29+=+log%285%2C+%28x%29%29+

+f%5E-1%28x%29+=+5%5Ex+

One way you can see they can not be equal is by thinking about x approaching zero from the negative side (i.e. consider negative x values). Only f%5E-1%28x%29 is defined on that region, and when x=0, f%5E-1%280%29+=+1. Now as x takes on positive values, f%5E-1%28x%29 becomes larger and larger positive values: (f%5E-1%282%29=25, f%5E-1%283%29=125, etc.). Looking at f%28x%29, it is only defined on x>0 and is negative for x < 1 and then reaches 0 at x=1, 1 at x=5, and then slowly rises for larger x values.


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