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

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Question 816208: How do you solve for x: log4(3x+5) = log2(4x-3)
Answer by Edwin McCravy(20056)   (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 =  
x = 
x = 
x = 

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
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