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Common Logarithms

A common logarithm is a logarithm which uses 1010 as its base. For example log10(1000)\log_{10}(1000) is equal to 33 because 10310^3 is equal to 1000.1000.

the Connection between the base and the exponent for common logarithms

Log base-10 can be written log10(),\log_{10}(), but since it is used so often, it has been shortened to lg().\lg(). Most calculators use this base when you press the log\log button. For positive numbers of aa, the definition of base-10 logarithm is as follows:

a=10bb=lg(a)a=10^b \quad \Leftrightarrow \quad b=\lg(a)

The numbers 0.01,0.1,1,100.01, \, 0.1, \, 1, \, 10 and 100100 can be written as powers of 10. In other words, 10-2,10-1,100,10110^{\text{-} 2}, \, 10^{\text{-} 1}, \, 10^{0}, \, 10^{1} and 10210^{2}. If you calculate base-10 logarithms from these examples, you will see that they indicate the exponents of the powers of ten.

xx 0.010.01 0.10.1 11 1010 100100
lg(x)\lg(x) lg(0.01)\lg(0.01) lg(0.1)\lg(0.1) lg(1)\lg(1) lg(10)\lg(10) lg(100)\lg(100)
== -2\text{-} 2 -1\text{-} 1 00 11 22

You can also calculate common logarithms on a calculator.