Math CentralQuandaries & Queries


Can you please explain Explain the difference between a logarithm of a product and the product of logarithms and give examples of each?

Hi Sharon,

In the first case, the logarithm of a product, you are to take the logarithm of something so you know it is


The rest of the expression says that this something is a product, say p x q, so you have

log(p x q)

The second expression, the product of logarithms, you have first a product

something x something

In this case the somethings are logarithms, maybe log(x) and log(y) so you have

log(x) x log(y).

I hope this helps,

Hi Sharon.

Log (ab) is the logarithm of a product, or in other words, logarithm(a product)

(Log a)(Log b) is the product of logarithms, or in other words, logarithm x logarithm.

For example,

Log 10 = Log (5 x 2), a logarithm of products in which you can use the product rule of logarithms so you know that Log (5 x 2) = (Log 5) +(Log 2)

(Log 5)(Log 2) is the product of two logarithms and it certainly does NOT equal Log 10.

Stephen La Rocque.>

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