What is the difference between the logarithm of a product? and the product of a logarithm? pls give examples.?

Question

What is the difference between the logarithm of a product? and the product of a logarithm? pls give examples.?

Answer 1

Logarithm of a product:

log(ab)

Product of a logarithm:

log(a) * log(b)

Answer 2

If you want to find A x B, add their logs, and take the anti log of that sum. I don't have a calc with me, so I'll wing it. logA + logB = C. antilogC = A x B. This was nifty back in the days of the slide rule when calcs were not here yet.

A number raised to a power;  A^B = anitlog(B x logA). This was even more nifty because most students had extreme trouble with powers. I hope this is what you were looking for.