Exponential and Logarithms

Exponential functions

Functions of the form:       f(x) = a^x

are known as exponential functions. The graphs of all such exponential functions pass through (0, 1).

Logarithms

Logarithms are another way of writing indices.

                       

     ·         If            a = b^c        then        c = log_ba

Example

                     We know that 10² = 100
                             
               Therefore              log₁₀ (100) = 2



You may often see ln x and log x written, with no base indicated. It is generally recognised that this is shorthand:

·         log_ex = lnx

·         log₁₀x = lgx or logx (on calculators)

Remember that 'e' is the exponential function, equal to 2.71828… (Donot EVER mistake it for a variable!)