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The Log (Logarithm) Calculator is used to calculate the logarithm log_{b}x for a base b and a number x.

The logarithm of a number x with respect to base b is the exponent to which b has to be raised to yield x. In other words, the logarithm of y to base b is the solution y of the following equation:

b^{y} = x

And for any x and b, there is:

x = log_{b}b^{x}

The logarithm to base b = 10 is called the common logarithm and has many applications in science and engineering. The natural logarithm has the constant e (approximately equal to 2.718281828) as its base. The binary logarithm uses base b = 2 and is prominent in computer science.