Question 710304: how do we graph y=ln(x)
Answer by jsmallt9(3758)   (Show Source):
You can put this solution on YOUR website! First, ln(x) is a logarithm. All logarithms have similar graphs so if you know what the graphs of logarithms of other bases look like then you have a basic idea of what the graph of ln(x) looks like.
Other than that you build a table of values and plot the points until you get a good idea how to "connect the dots" into a smooth curve. Since x is the argument of a logarithm and since arguments of logarithms, no matter what the base, must be positive, the domain is all positive numbers. This means: Pick only positive numbers for x when building the table of values.
If you have a calculator with a button for ln then you do not need to be choosy about what (positive) x values to pick when building your table of values. If you do not have such a calculator then you should pick x values whose ln you can figure out by hand. IOW, without a calculator with ln pick x values that are known powers of the base of ln, e. For example:
 so ln(1) = 0 making (1, 0) a point on the graph
 so ln(e) = 1 making (e, 1) a point on the graph
 so ln(e^2) = 2 making ( , 2) a point on the graph
 so ln(1/e) = -1 making (1/e, -1) a point on the graph
etc.
For the number "e" use 2.8 as an approximation.
P.S. If you use the Calculator program that comes with Windows, you can find ln's with it. If you do not see a button for ln when you start the program just click on the "View" menu and then click on "Scientific". This gives you a bigger display with a lot more buttons. One of them will be ln.
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