is "log(a) + log(b) = log (a+b)" true?

Let's suppose that it is true....then, by a property of logs, we can wtite

log(ab) = log(a + b)

But, in general, ab ≠ a + b.  Thus, this "identity" isn't true.........

Almost. 

Log(a) + log(b) = log(a*b)  //not log(a+b)

the formulary page on this sitecan be very useful.

Look here.

http://web2.0calc.com/formulary/math/algebra/log