SOLUTION: what is (are) the solution(s) of the equation log sub 4 4x+2 log sub4(x+3)=2

log4(4x) + 2·log4(x + 3) = 2

Get the left side to a single logarithm.

Use the rule

 n·logBA = logBAn  

to rewrite the second term:

log4(4x) + log4(x + 3)2 = 2

Use the rule:

 logBA + logBC = logB(AC) to rewrite the
whole left side:

        log4[4x(x + 3)2] = 2

Use the rule:

logBA = C can be rewritten as A = BC 

to rewrite the equation:

          4x(x + 3)2 = 42

    4x(x + 3)(x + 3) = 16

4x(x2 + 3x + 3x + 9) = 16

     4x(x2 + 6x + 9) = 16

To make things easier, divide both sides by 4

      x(x2 + 6x + 9) = 4     

       x3 + 6x2 + 9x = 4

   x3 + 4x2 + 9x - 4 = 0 

There is no easy way to solve that by hand, so we
use a TI-82 or higher calculator and get

            x = 0.3553013976 
Edwin