This section is a quick introduction to logarithms and notation (and ways to avoid the notation).
Logarithms are perhaps the most artificial feeling function in our library of functions. If we remember, exponential functions were one-to-one (passing the vertical and horizontal line tests) and are thus invertible. Logarithms are precisely the inverse functions that correspond to the exponential functions of our last topic.
Notation and how to avoid it!
It turns out that logarithms are extremely useful in many unexpected ways.
Nonetheless, until we are comfortable with logarithmic notation, it can often be helpful to translate a logarithm from it’s log notation to the corresponding exponential function that they are the inverses of. The notation would be stated as “log base of is equal to ”. The corresponding exponential form for this equation would then be . In particular, is a function that is the inverse function of the exponential . Thus, utilizing the inverse function property, we have;