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A useful property of logarithms states that the logarithm of a product of two quantities is the sum of the logarithms of the two factors. In symbols, logo(XY)=logo(x)+logo(y). (x y) = log b (x) + log b
A useful property of logarithms states that the logarithm of a product of two quantities is the sum of the logarithms of the two factors. In symbols, logo(XY)=logo(x)+logo(y). (x y) = log b (x) + log b
The rule is that you keep the base and add the exponents. Well, remember that logarithms are exponents, and when you multiply, you're going to add the logarithms. The log of a product is the sum of the logs.
Can you distribute log on log(x+y)? In general, no. The logarithm of a sum is as simplified as it gets, unless the sum itself can in some way be simplified. (For instance log(5 + 3) = log(8)).
Rule one: if LN(a) = LN(b), then a must equal b. Rule two: LN(ab) = LN(a) + LN(b) for all positive real numbers. Therefore, LN does not distribute over its argument.
To convert a number from a natural to a common log, use the equation, LN(x) = log(x) ÷ log(2.71828).

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