*Log Calculator* is an online math tool used to calculate the Log value for the given Logarithm number with respect to the given or natural base values

### Logarithm

The logarithm of a number to a given base is the exponent by which the base has to be raised to produce that number. For example, the logarithm of 1000 to base 10 is 3, because 1000 is 10 to the power 3: 1000 = 10^{3} = 10x10x10. More generally, if x = by, then y is the logarithm of x to base b, and is written logb(x), so log10(1000) = 3

**More examples for Log Calculation**

y = 1000 means y = 10^{3}; therefore, Log 1000 = 3

y = 100 means y = 10^{2}; therefore, Log 100 = 2

y = 10 means y = 10^{1}; therefore, Log 10 = 1

y = 1 means y = 10^{0}; therefore, Log 1 = 0

y = 0.1 means y = 10^{-1}; therefore, Log 0.1 = - 1

y = 0.01 means y = 10^{-2}; therefore, Log 0.01 = - 2

y = 0.001 means y = 10^{-3}; therefore, Log 0.001 = - 3

The above example illustrates several properties of logarithms. Numbers greater than 1 have positive logarithms; numbers less than one but greater than zero have negative logarithms. Logarithms do not exist for zero or negative numbers, because you cannot raise 10 to any power such that the result will be zero or a negative number