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Logarithms

TRY IT:

Rewrite this as a bunch of little logs:

log( ( z w^8 ) / ( y x^6 ) )

They only get a little messier...

Ln( ( 5x^2 z ) / ( w^3 y^4 ) )^6 = 6 * Ln( ( 5x^2 z ) / ( w^3 y^4 ) ) = 6[ Ln( 5 ) + 2 * Ln( x ) + Ln( z ) - 3 * Ln( w ) - 4 * Ln( y ) ] = 6 * Ln( 5 ) + 12 * Ln( x ) + 6 * Ln( z ) - 18 * Ln( w ) - 24 * Ln( y )

The only other thing they'll throw at you is roots...  When this happens, just switch over to exponential notation:

square root( x ) = x^( 1 / 2 )

 

YOUR TURN:

Rewrite these as a bunch of little logs:
 

log( 3x^2 w^4 )
 

log( ( w^( 2 ) x ) / ( 7z^3 ) )^4
 

log( square root( ( 5w^7 ) / ( 3x^2 ) ) )

* remembersquare root( x ) = x^( 1 / 2 )