This details methods by which we can calculate logarithms by hand

W Blaine Dowler:

A logarithm can be defined as follows: if bx = y, then x = logb y. In other words, the logarithm of y to base b is the exponent we must raise b to in order to get y as the result. Exponentiation will “undo” a logarithm, and vice versa: blogb x = logb (bx) = x. The logarithm inherits certain useful properties directly from exponents.