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When we take the logarithm of both sides of ELN(XY)=ELN(x)+LN(y), we obtain LN(ELN(XY))=LN(ELN(x)+LN(y)). The logarithms and exponential cancel each other out (equation (4)), giving our product rule for logarithms, LN(XY)=LN(x)+LN(y).
In mathematics, the logarithmic mean is a function of two non-negative numbers which is equal to their difference divided by the logarithm of their quotient. This calculation is applicable in engineering problems involving heat and mass transfer.
The logarithm of the ratio of two quantities is the logarithm of the numerator minus the logarithm of the denominator. Rule 3: Power Rule. The logarithm of an exponential number is the exponent times the logarithm of the base. Rule 4: Zero Rule. The logarithm of 1 such that b > 0 b > 0 b>0 but b1 equals zero.
A logarithm is the power to which a number must be raised in order to get some other number (see Section 3 of this Math Review for more about exponents). For example, the base ten logarithms of 100 is 2, because ten raised to the power of two is 100: log 100 = 2.

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