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    Logarithm Calculator (Calculate log(x) with any base)

    The logarithm (log) operation in mathematics is the inverse to exponentiation, meaning that the log of a number is the exponent to which another fixed number called a "base" was raised to produce the number. For example log232 = 5, since 25 = 32. This is an example of a simple logarithm as it basically counts the number of multiplications of the sa...

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    Certain logarithms can be easy to compute in your mind, e.g. log10(1000) = 3 since 10^3 = 1000. A general solution is to calculate logs using power series or the arithmetic-geometric mean. A pre-calculated table can also be of use if only a range of bases and logarithms are of interest on a daily basis. For anything else it is most convenient to us...

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    log264 = 6, since 26 = 2 x 2 x 2 x 2 x 2 x 2 = 64. That's a log with base 2, log2. log327 = 3, since 33= 3 x 3 x 3 = 27. That's a log with base 3. log101000 = 3, since 103= 10 x 10 x 10 = 1000. That's a log with base 10.

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    Logarithmic scalesare often used when representing wide-ranging measurements in a visually compelling graph. A prominent example is the decibel scale in which the unit (dB) expresses log-ratios of signal power and amplitude - mostly used for sound waves. pH is a well-known chemistry scale for measuring acidity. Discrete logarithms have uses in publ...

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