15.2 Solving Exponentail Functions

Solving exponential equations can be carried out by:

a) Plotting an accurate graph and reading solution from the graph

b) Using an algebraic solution

c) Using a graphing calculator

EXAMPLE : Solve each of the following equations a) 2^x= 10 b) 2 x 3^x + 1 = 40

SOLUTION:

a) To start with we need to plot a graph of the function f(x) = 2^x, from where we will then simply read the solution from the graph (i.e. along the x-axis). From our graph we therefore have that if 2^x=10 then x = 3.3

b) To solve the equation 2 x 3^x+ 1 = 40 using the TI-83 calculator. Type this into your calculator: solve(2 x 3^x + 1 -40,x,2). This method of using your calculator give the solution x = 2.70