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Logarithms

Here's how you can use these in Calculus to make your life a lot easier:

Check this guy out:

Ln( ( xwz ) / ( y^2 ) ) ... This is a bit of a mess.
 

Having logs of little things will be much easier, so let's use our rules:


Ln( ( xwz ) / ( y^2 ) ) = Ln( xwz ) - Ln( y^2 ) ... rule 2 ... = Ln( x ) + Ln( w ) + Ln( z ) - 2 * Ln( y ) ... the addition was rule 1 ... the subtraction is rule 3 ... Done!
 

Trust me on this -- the Calculus on this would take about 10 seconds!

Let's do another one:


log( ( x^2 w ) / ( y z^3 ) ) = log( x^2 w ) - log( y z^3 ) ... rule 2 ... = log( x^2 ) + log( w ) - ( log( y ) + log( z^3 ) ) ... both parts were rule 1 ... Be careful with the minus sign ... = 2 * log( x ) + log( w ) - log( y ) - 3 * log( z ) ... the first part and the last part are rule 3 ... I distributed the " - "