SOLUTION: f(x) = ln (x-e)-1 how do i sketch the graph and find the domain? i really don't understand the problem. all that is in my book is how to graph logarithms not natural logs. is it th

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: f(x) = ln (x-e)-1 how do i sketch the graph and find the domain? i really don't understand the problem. all that is in my book is how to graph logarithms not natural logs. is it th      Log On


   

Question 723028: f(x) = ln (x-e)-1 how do i sketch the graph and find the domain? i really don't understand the problem. all that is in my book is how to graph logarithms not natural logs. is it the same thing? please if you have the knowledge please spare a minute. good karma will be awarded.
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
Logarithms can have any positive number except 1 as a base. Natural logarithms are just a logarithm with a specific base, the number we call "e". In other words, ln%28x%29+=+log%28e%2C+%28x%29%29.

The graphs of all logarithms with a base which is greater than 1 have similar-looking graphs. Here's the graphs of y+=+log%28%28x%29%29 (whose base is 10) in green, y+=+log%285%2C+%28x%29%29 in blue and y+=+ln%28x%29 in red:

The main difference in the three is how sharply they curve. The higher the base is the more sharply the graph curves. (Note: The actual graphs do not intersect the y-axis. If it looks like they do, it is just because of a flaw in algebra.com's graphing software.)

For the graph of f(x) = ln(x-e)-1 we just take the graph of y = ln(x) and preform the appropriate transformations. In f(x) we have "x-e" instead of just "x" so the graph of f(x) will be shifted to the right by "e" (which is about 2.8). The "-1" in f(x) will shift the graph down 1. So to sketch f(x), take the graph of ln(x) and shift it to the right by about 2.8 and down by 1.