Expert: Steve Holleran - 7/23/2008

Question
i was asked to solve for x for this equation:
7^(-9x) = 4^(x+6)

could you help me, please?
thanks for your time

Answer
Hi Mimi,

Okay, since this is an exponential equation, we can solve it using logarithms.  You can use base 10 logs, (log) , or base e logs , (ln), because these are the two available to you on a calculator or in tables.

The algebra set-up of the solution would go like this:

                   7^(-9x) = 4^(x + 6)

                ln[7^(-9x)] = ln[4^(x + 6)]

               -9x * ln 7   = (x + 6) * ln 4

               -9x * ln 7   = x * ln 4 + 6 * ln 4
      
               -9x * ln 7 - x * ln 4 = 6 * ln 4

               x(-9 * ln 7 - ln 4) = 6 * ln 4

               x = [6 * ln 4] / [-9 * ln 7 - ln 4]

At this point, just get the values for the lns and calculate it out.
I came up with x = -0.4401


Hope this helps you out.
Steve