log(a+b)

log(a)*log(b)

NO!!!!....Guest's answer is incorrect.....!!!!

To prove this we only need one counter-example :

log (1000 + 100)  ≠   log1000 * log 100     [verify this for yourself ]

log (a * b)   =    log a + log b     is a valid property....but, unfortunately.....log (a + b)    just remains log (a + b) .....!!!!!

Thank you CPhill for your clarification.