# How does a logarithm work?

**logarithm**is the inverse function to exponentiation. That means the

**logarithm**of a given number x is the exponent to which another fixed number, the base b, must be raised, to produce that number x.

Also know, how are logarithms calculated?

**Logarithm**, the exponent or power to which a base must be raised to yield a given number. Expressed mathematically, x is the **logarithm** of n to the base b if b^{x} = 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.

**Log 0**is undefined. The result is not a real number, because you can never get zero by raising anything to the power of anything else. You can never reach zero, you can only approach it using an infinitely large and negative power. The real logarithmic function logb(x) is defined only for x>

**0**.

Consequently, what is log10 equal to?

Mathematically, **log10**(x) is **equivalent to log(10**, x) . See Example 1. The logarithm to the base 10 is defined for all complex arguments x ≠ 0. **log10**(x) rewrites logarithms to the base 10 in terms of the natural logarithm: **log10**(x) = ln(x)/ln(10) .

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 100 is 2, because ten raised to the power of two is 100: log 100 = 2.