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Some Special Logs

Here's another one:

You've seen by now that this is a very special guy...

y = e^( x )

Here's his graph (grab a calculator!):

x: -1 , 0 , 1 ... y: e^( -1 ) = approximately .37 , 1 , e^( 1 ) = approximately 2.7 y = e^( x ) ... includes the points ( -1 , 1 / e ) , ( 0 , 1 ) and ( 1 , e )

He's got a very special inverse, too...

y = log to the base e( x )

In fact, he's so special that he gets his own log name AND button on your calculator:

The natural log: y = Ln( x )
button: Ln or ln
* Notice that his inverse, e^( x )

 , is right above him!

So, what's his graph?

y = Ln( x ) graph of y = Ln( x ) ... includes the points ( 1 / e , 1 ) , ( 1 , 0 ) and ( e , 1 )

Remember that this guy's graph will NOT cross the y-axis as it goes down!  It will get closer and closer, but never touch or cross.