An exponential function is a mathematical function in the form f (x) = a^x, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0. For example Given the function f(x)=2^x, find f(−2). To evaluate any function, we simply have to use the given input. Therefore, we have: f(-2)= 2^(-2)= 1/2^2 = ¼.
Logarithmic functions are the inverses of exponential functions, and any exponential function can be expressed in logarithmic form. Similarly, all logarithmic functions can be rewritten in exponential form. Logarithms are really useful in permitting us to work with very large numbers while manipulating numbers of a much more manageable size. There are some important rules about logarithmic functions but the most important rule is log a (p q) = q log a p. For example If 2 log x = 4 log 3, then find the value of ‘x’. 2 log x = 4 log 3 Then I will divide each side by 2. log x = (4 log 3) / 2. log x = 2 log 3 log x = log 32 log x = log 9 x =9
Also both of the exponential and logarithmic functions are used in our daily lives frequently. We use exponential functions in biology while determining microorganisms in culture, human population and compound interest. We also use logarithmic functions in measuring earthquakes, measuring sound levels, and learning the acidity(pH). As it is obvious logarithmic and exponential functions are in real life and scientists and engineers use them quite often.