There are three big important properties of logarithms that each come from a property of exponents. Here are the properties with their corresponding exponent properties. 
  
Logarithm Properties	

loga(MN)=logaM+logaN 	

loga(M/N)=logaM-logaN 	

loga(Mp)=plogaM 	

	Exponential Properties	

axay=ax+y 	

ax/ay=ax-y 	

(ax)p=apx