Log(ab) = Log(a) + Log(b) is the correct formula. According to the laws of logarithm, the logarithm of product of two numbers is equal to the sum of logarithms of two numbers.

If a=10 and b= 1000, then

Log(10*1000) = Log(10) + Log(1000)

Log(10000) = Log(10) + Log(1000)

4 = 1+3

4=4

Both the sides are equal so, Log(ab) = Log(a) + Log(b).

If a=10 and b= 1000, then

Log(10*1000) = Log(10) + Log(1000)

Log(10000) = Log(10) + Log(1000)

4 = 1+3

4=4

Both the sides are equal so, Log(ab) = Log(a) + Log(b).