Examples of logarithms:
log_{2} 8 = 3 since 8 = 2^{3}
log_{10} 0.01 = -2 since 0.01 = 10^{-2}
log_{5} 5 = 1 since 5 = 5^{1}
log_{b} 1 = 0 since 1 = b
From the above illustration, it is evident that a logarithm is an exponent. 3^{4} is called the exponential form of the number 81. In logarithmic form, 3^{4} would be expressed as log 81 = 4, or the logarithm of 81 to the base 3 is 4. Note the symbol for taking the logarithm of the number 81 to a particular base 3, is log3 81, where the base is indicated by a small number written to the right and slightly below the symbol log.