SOLUTION: <pre>Hi I am having problems with this: Solve the following equation: 3^x = 15·4^x-2</pre>

Hi I am having problems with this: Solve the following equation:

3x = 15·4x-2

We need two rules of natural logarithms:

(1)   ln(AB) = ln(A) + ln(B)

(2)   ln(AN) = N·ln(A) 
   
-------------------------------------

          3x = 15·4x-2

Take the natural logarithm of both sides:

      ln(3x) = ln(15·4x-2)

Use rule (2) on the left side and rule (1) on
the right side:

     x·ln(3) = ln(15) + ln(4x-2)

Use rule (2) on the last term on the right 

     x·ln(3) = ln(15} + (x-2)·ln(4)

To make things easier, let
A = ln(3), B = ln(15) and C = ln(4)

         x·A = B + (x-2)·C 
          Ax = B + C(x-2)
          Ax = B + Cx - 2C
     Ax - Cx = B - 2C
    x(A - C) = B - 2C
           x = (B - 2C)/(A - C)

Now replace A by ln(3), B by ln(15), 
and C by ln(4):

           x = [ln(15)-2·ln(4)]/[ln(3)-ln(4)]

Now get your calculator and get:

           x = .2243397393

Edwin