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Logarithms

This is just a formula game.  In Calculus, these rules can make an impossible problem really easy!
 

1 ) log base b( xy ) = log base b( x ) + log base b( y )

 

Here's an example that you can double-check
on your calculator to see if this really works:

log 10 = log( 2 * 5 ) = log( 2 ) + log( 5 )

 

2 ) log base b( x / y ) = log base b( x ) - log base b( y )

 

Check this on your calculator:


Ln( 25 ) = Ln( 50 / 2 ) = Ln( 50 ) - Ln( 2 )

 

Finally, here's our old friend:

3 ) log base b( x^p ) = p * log base b( x )

 

Check this on your calculator:


log( 9 ) = log( 3^2 ) = 2 * log( 3 )