Explain the difference between a logarithm of a product and the product of logarithms and give examples of each.
2007-01-16 08:21:28 · 3 answers · asked by Just Wondering 5 in Science & Mathematics ➔ Mathematics
log(xy) is the logarithm of a product,
and
(logx)(logy) is the product of logarithms
these 2 are very different check it out:
log ((1)e) = log(e) =1
but
log(1)log(e) = 0(1) =0 .
2007-01-17 01:53:12 · answer #1 · answered by Anonymous · 1⤊ 0⤋
A product of logaithms is nothing. You are just stuck with it. For instance (ln 2 )^2 is just itself BUT ln 2 + ln 3 = ln 6. Got it?
2007-01-16 16:27:25 · answer #2 · answered by gianlino 7 · 1⤊ 0⤋
They are simply different.
Logarithm of products:
log(X * Y) can be expressed as log(X) + log(y) due to logarithmic identities.
Product of logarithms:
log(X)^2 = log(X) * log(X)
2007-01-16 16:41:25 · answer #3 · answered by merlinn31 2 · 1⤊ 0⤋