How do you graph ln(x)?

Question

2498 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-06-28T21:29:59

Reflect the graph of #e^x# in the line #y=x#...

First think about how you can graph #e^x#

Note that #e ~~ 2.71828182844#, so #e^x# is a smooth exponential curve passing through:

#(0, 1)#

#(1, e) ~~ (1, 2.718)#

#(2, e^2) ~~ (2, 7.389)#

#(3, e^3) ~~ (3, 20.0855)#

...

#(-1, e^(-1)) ~~ (-1, 0.3679)#

#(-2, e^(-2)) ~~ (-2, 0.1353)#

#(-3, e^(-3)) ~~ (-3, 0.0498)#

...

So it looks like this:
graph{e^x [-11.04, 8.96, -1.28, 8.72]}

To get the graph of its inverse #ln(x)#, we can reflect this graph in the diagonal line #y=x# to get:
graph{ln x [-5.04, 14.96, -6.96, 3.04]}