SOLUTION: How do you solve for x: log<sub>4</sub>(3x+5) = log<sub>2</sub>(4x-3)

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: How do you solve for x: log<sub>4</sub>(3x+5) = log<sub>2</sub>(4x-3)      Log On


   

Question 816208: How do you solve for x: log4(3x+5) = log2(4x-3)
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
log4(3x+5) = log2(4x-3)

Let each side equal to y         

log4(3x+5) = y      and      log2(4x-3) = y
        4y = 3x+5   and              2y = 4x-3
     (22)y = 3x+5   
       22y = 3x+5
      2y·2 = 3x+5
     (2y)2 = 3x+5

Substitute 4x-3 for 2y

      (4x-3)² = 3x+5

   16x²-24x+9 = 3x+5
   16x²-27x+4 = 0

x = %28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29+ 
x = %28-%28-27%29+%2B-+sqrt%28+%28-27%29%5E2-4%2816%29%284%29+%29%29%2F%282%2816%29%29+
x = %2827+%2B-+sqrt%28729-256%29%29%2F32+
x = %2827+%2B-+sqrt%28473%29%29%2F32+

Using a calculator:

x = 1.523392599 and .1641074009

only x = 1.523392599 checks.  The other answer causes the right side
to give the log of a negative number, which is not a real number.

Edwin