document.write( "Question 710304: how do we graph y=ln(x) \n" ); document.write( "

Algebra.Com's Answer #437077 by jsmallt9(3758) $\"\"$ $\"About$

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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.

\n" ); document.write( "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.

\n" ); document.write( "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:
\n" ); document.write( " $\"e%5E0+=+1\"$ so ln(1) = 0 making (1, 0) a point on the graph
\n" ); document.write( " $\"e%5E1+=+e\"$ so ln(e) = 1 making (e, 1) a point on the graph
\n" ); document.write( " $\"e%5E2+=+e%5E2\"$ so ln(e^2) = 2 making ( $\"e%5E2\"$ , 2) a point on the graph
\n" ); document.write( " $\"1%2Fe+=+e%5E%28-1%29\"$ so ln(1/e) = -1 making (1/e, -1) a point on the graph
\n" ); document.write( "etc.
\n" ); document.write( "For the number \"e\" use 2.8 as an approximation.

\n" ); document.write( "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. \n" ); document.write( "

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