8.1B  Solving Exponential Equations with e

Example 1

     Find the value of x.  Keep the answer in exact form (no decimals).

      e3x - 2 = 1

 Solution

      e3x - 2 = 1

      e3x  = 3                  add 2 to both sides

    ln e3x = ln 3              using the property for ln and e:    ln ex = x

    3x = ln 3                 divide by 3

      x = (ln 3)/3

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Example 2

      Find the value of x.  Keep answer in exact form (no decimals).

      e4x - 3 = 19

Solution

      e4x - 3 = 19

   ln e4x - 3 = ln 19          using the property for ln and e:   ln ex = x

      4x - 3 = ln 19          add 3 to both sides

      4x = ln 19 + 3          divide by 4

        x = (ln 19 + 3)/4

Example 3

      Find the value of x.  Keep answer in exact form (no decimals)

     2[e3x-1] - 7 = 13

Solution

    2[e3x-1] - 7 = 13

    2[e3x-1] = 20

    [e3x-1] = 10

    ln[e3x-1] = ln 10

   3x - 1 = ln 10

   3x = ln 10 + 1

      x = (ln 10 + 1) / 3