## taking the logarithm of the euler product

can some one explain to me how is taking the logarithm of euler product gives you -sum(p)[log(1-p^s)]+log(s-1)=log[(s-1)z(s)]?

my question is coming after encoutering this equation in this text in page number 2: http://claymath.org/Millennium_Prize...escription.pdf

btw, does taking a logarithm out of a product gives you the summation or what?