Expert: Steve Holleran - 6/17/2007

Question
Steve,  I am having a hard time calculating and plotting the following functions:  
Exponential function e^2 and logarithmic function log x, show the effect if x is doubled.  Graph these.

Answer
Hello Heather,

For the first one, y = e^2, you just have to realize that e^2 is a constant (about 7.4), so you are graphing a horizontal line through y-level e^2.

For the second one, y = log x, this means the base 10 log of x.  Some points would be :

   (1,0)    (10, 1)    (100, 2)   (1000, 3)   etc.

The graph would be asymptotic to the negative y-axis, would pass through (1,0), then rise slowly through the points I mentioned; it would also be concave down for all values.

For x being doubled, you have y = log (2x)  and by the properties of logarithms, this is the same as :

     y = log(2x) = log(2)   log(x)

So you can see, its the same as y = log x with a vertical shift of (log 2) being added, so the entire log x graph would be raised up log 2 units (about 0.3).

I hope this was what you were looking for.  If not, please let me know.

Steve Holleran