In mathematics, the logarithm of a number is the exponent by which another fixed value, the base, must be raised to produce that number. For example, the logarithm of 1000 to base 10 is 3, because 1000 …

Sometimes a logarithm is written without a base, like this: This usually means that the base is really 10. It is called a "common logarithm". Engineers love to use it. On a calculator it is the "log" button.

The base b logarithm of a number is the exponent that we need to raise the base in order to get the number. The logarithm of the multiplication of x and y is the sum of logarithm of x and logarithm of y. …

Expressed mathematically, x is the logarithm of n to the base b if bx = n, in which case one writes x = log b n. For example, 2 3 = 8; therefore, 3 is the logarithm of 8 to base 2, or 3 = log 2 8.

To calculate the logarithm of a number x with base b, enter your values below. Did we solve your problem today? The log calculator (logarithm) calculates the value of a logarithm with an arbitrary base.

Since taking a logarithm is the opposite of exponentiation (more precisely, the logarithmic function logb x log b x is the inverse function of the exponential function bx b x), we can derive the basic rules for …

To avoid ambiguity, it is safest to use "log" to refer to base 10 logarithms and "ln" or "natural log" to refer to base e logarithms. In other words, "log (x)" typically indicates log 10 (x) and ln (x) indicates log e (x).

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 logarithm of …

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An exponential equation is converted into a logarithmic equation and vice versa using b x = a ⇔ log b a = x. A common log is a logarithm with base 10, i.e., log 10 = log.