(mathematics) For a number x {\displaystyle x} , the power to which a given base number must be raised in order to obtain x {\displaystyle x} . Written log b ⁡ x {\displaystyle \log _{b}x} . For example, log 10 ⁡ 1000 = 3 {\displaystyle \log _{10}1000=3} because 10 3 = 1000 {\displaystyle 10^{3}=1000} and log 2 ⁡ 16 = 4 {\displaystyle \log _{2}16=4} because 2 4 = 16 {\displaystyle 2^{4}=16} .