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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
The below are the logarithm examples to understand the how to find logrithm of numbers.
y = 1000 => y = 10^{3} => Log 1000 = 3
y = 100 => y = 10^{2} => Log 100 = 2
y = 10 => y = 10^{1} => Log 10 = 1
y = 1 => y = 10^{0} => Log 1 = 0
y = 0.1 => y = 10^{1} => Log 0.1 =  1
y = 0.01 => y = 10^{2} => Log 0.01 =  2
y = 0.001 => y = 10^{3} => 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. The above examples & formulas may useful to to know how to take logarithm for a number, however, when it comes to quick calculations, this math log calculator help users to perform such computations as quick as possible.
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