Logarithmic expressions allow for linear modeling of exponential data. These expressions are also often compressed to avoid multiple repetitions of the logarithm function in a single expression. They must be expanded in certain cases, however, to allow for other operations, such as integration. This yields smaller, simpler expressions to be operated on instead of complex rational and exponential variants. Several simple logarithm rules expand logarithms into their uncompressed forms.
Instructions
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1
Move any exponent that the logarithm is raised to by placing it in front of the logarithmic expression. Example, Ln(2)^2 = 2 * ln (2).
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2
Separate any logarithmic function containing a rational expression into two logarithmic functions with the term in the denominator being subtracted from the term in the numerator. Example, ln(2/3) = ln(2) - ln(3).
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3
Separate any multiplicative terms left within the logarithmic function into the addition of each term in a logarithm. Example: ln(3x * 4y) = ln(3x) + ln(4y).