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Logarithms are a convenient way to express large numbers. (The base-10 logarithm of a number is roughly the number of digits in that number, for example.) Slide rules work because adding and subtracting logarithms is equivalent to multiplication and division. (This benefit is slightly less important today.)

Multiplication.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.

The sum of the logs is the log of the product. The log of a sum cannot be simplified. The log of a difference is NOT the difference of the logs. The difference of the logs is the log of the quotient.

How Many Types Of Logarithms Are There?Common logarithm: These are known as the base 10 logarithm. It is represented as log10.Natural logarithm: These are known as the base e logarithm. It is represented as loge.

Rules of LogarithmsRule 1: Product Rule.Rule 2: Quotient Rule.Rule 3: Power Rule.Rule 4: Zero Rule.Rule 5: Identity Rule.Rule 6: Log of Exponent Rule (Logarithm of a Base to a Power Rule)Rule 7: Exponent of Log Rule (A Base to a Logarithmic Power Rule)

Logs of the same base can be added together by multiplying their arguments: log(xy) = log(x) + log(y). They can be subtracted by dividing the arguments: log(x/y) = log(x) - log(y).

Logs of the same base can be added together by multiplying their arguments: log(xy) = log(x) + log(y). They can be subtracted by dividing the arguments: log(x/y) = log(x) - log(y).