Examples of logarithms:

log₂  8 = 3                                            since    8 = 2³

log₁₀  0.01 = -2                                    since    0.01 = 10^-2

log₅  5 = 1                                            since    5 = 5¹

log_b  1 = 0                                            since    1 = b

From the above illustration, it is evident that a logarithm is an exponent. 3⁴ is called the exponential form of the number 81.  In logarithmic form, 3⁴ 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.