2.2.1—Log laws

For a,b>0 and base k>0,k≠1, log_k(ab)=log_k a+log_k b, log_k(a/b)=log_k a−log_k b and log_k(a^p)=p log_k a.

Check every argument is positive before combining logs. Change of base gives log_k a=ln a/ln k and is useful when the calculator uses natural logs.

log₂(8x)−log₂x=3 for x>0, because the ratio is 8.

log(a+b) is not log a+log b; the product law does not apply to sums.