What are some properties of ln x + ln y?


Quick Answer

The mathematical property associated with ln x + ln y is the product rule of natural logarithms, expressed as ln(x ? y) = ln(x) + ln(y). The rule is used for adding together any two logarithm expressions that are to the same base, which for the natural logarithm is the base e.

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What are some properties of ln x + ln y?
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Full Answer

For example, the expression ln(2) + ln(3) uses the product rule to become the ln(2 * 3), which is equal to the ln(6). The quotient rule for natural logarithms is related to the product rule and is used when a natural logarithm is subtracted from another natural logarithm. This rule is expressed as ln(x / y) = ln(x) - ln(y).

Other rules used to evaluate natural logarithm expressions that include both an x and y variable include the power rule, which is expressed in mathematical notation as ln(x^y) = y ? ln(x). Additional general identities used when evaluating natural logarithms include the derivative, which for the function f(x) = ln(x) is always equal to f'(x) = 1/x, and the integral, which for the same function is x ? (ln(x) - 1) + C. When the value for x in ln(x) is less than or equal to zero, the value is undefined. The natural logarithm of one is equal to zero. The limit of ln(x) as x approaches infinity is defined as infinity.

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