Give an example of an exponential function Find this exponential function's inverse which will be a logarithmic function Plot the graph of both the functions?

An exponential function can be is of the form f(x) = a*(b^x). Some examples are f1(x) = 3*(10^x), or f2(x) = e^(-2*x). Note that the latter still fits the format, with b = e^(-2). The inverse is the logarithmic function. So for y = f1(x) = 3*(10^x), reverse the x & y, and solve for y:

• x = 3*(10^y)
• log(x) = log(3*(10^y)) = log(3) + log(10^y) = log(3) + y*log(10) = y*1 + log(3)
• y = log(x) - log(3) = log(x/3)

The second function: y = e^(-2*x), the inverse is: x = e^(-2*y).

• ln(x) = ln(e^(-2*y)) = -2*y*ln(e) = -2*y*1
• y = -ln(x)/2 = ln(x^(-1/2))

See related link for an example graph.