8.1A  Solving Exponential Functions

Solving Exponential Functions

   When solving exponential functions, we will have to use some of the special rules for these functions. 

     Rule:   If bx = by, then x = y    If the bases are the same, the exponents are equal.

Example 1

   2-x = 16              Notice the bases are not the same, but 16 can be rewritten as 24.

   2-x = 24              The bases are now 2, so the exponents are equal.

  -x = 4

    x = -4

Check your answer       Make sure you check your answer to determine if it is a solution to the equations.

  2(-(-4))  = 16

  24 = 24

------------------------------------------------------------------------

Example 2

   9(-x + 15) = 27x          In this example, we need the same base to apply the rule.

   32(-x + 15)  = 33x         Rewrite 9 and 27 as base 3.  Now we have the same base and we can apply the rule.

  2(-x + 15) = 3x       Solve for x.

  -2x + 30 = 3x

           30 = 5x

             6 = x            

Check your answer      Make sure your answer is valid.

   9(-6 + 15) = 276

    99 = 276

    32(9) = 33(6)

    318 = 318               Solution is valid