Logarithm | Common Logarithm | Natural Logarithm | Evaluating or Simplifying Logarithm

Logarithmic function is the inverse of exponential function. Hence, any exponential expression can be rewritten into a logarithmic expression.
Instead of 'log to the base a of N is equal to the exponent x', a logarithmic equation can be interpreted as 'to what exponent x do you raise the base a to get the argument N'.
Therefore, evaluating a logarithmic function is equivalent to solving for the exponent.
Common logarithm is logarithm to the base 10. However, the base 10 is usually not written such that 'log to the base 10 of x' is the same as 'log of x'.
Natural logarithm is logarithm to the base e (Euler's number). 'Log to base e' is usually abbreviated as ln such that 'log to the base e of x' is the same as 'ln of x'.