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It's really easy to just do these guys in your head.


Here's how it works:

       Guys that start out on the top...

log( x^( 2 ) * w / y * z^( 3 ) )

       end up with " + " signs in front of them:

2 * log( x ) + log( w ) - log( y ) - 3 * log( z ) ... the first and second guys are " + "

       Guys that start out on the bottom...

log( x^( 2 ) * w / y * z^( 3 ) )

       end up with " - " signs in front of them:

= 2 * log( x ) + log( w ) - log( y ) - 3 * log ( z ) ... the last two guys in this equation are negative

Then you just have to deal with the exponents.  Easy!
 

Let's do this guy in one shot:

Ln( x^( 7 ) * w^( 2 ) / y^( 4 ) * z ) = 7 * Ln( x ) + 2 * Ln( w ) - 4 * Ln( y ) - Ln( z )