You're going to use rule #3 in Calculus a lot -- again to make impossible problems doable.  I'm not going to lie...  They still won't be easy, but, at least you'll be able to do them!
 

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


In Calculus, having a variable in the base AND in the exponent is bad news.

Remember that this guy lets you bring those variables down in front:


Ln( sin( x ) )^x = x * Ln( sin( x ) )

 

Ln( x )^( Ln( x ) ) = Ln( x ) * Ln( x)

 


TRY IT:

Ln( 2x^2 + 5 )^( x^3 ) =
 

Ln( cos( 7x ) )^( 2x ) =