Question 710304
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.<br>
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.<br>
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:
{{{e^0 = 1}}} so ln(1) = 0 making (1, 0) a point on the graph
{{{e^1 = e}}} so ln(e) = 1 making (e, 1) a point on the graph
{{{e^2 = e^2}}} so ln(e^2) = 2 making ({{{e^2}}}, 2) a point on the graph
{{{1/e = e^(-1)}}} 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.<br>
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.