Hi

log (x+2) + log (2x-3) =2 

log (x+2)(2x-3) = 2

(x+2)(2x-3) = 100

 2x^2 +x -100 = 0

x = 6.82548584904245    x > 0

 


 
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation  (in our case ) has the following solutons:

  

  

  

  For these solutions to exist, the discriminant  should not be a negative number.

  

  First, we need to compute the discriminant : .

  

  Discriminant d=801 is greater than zero. That means that there are two solutions: .

  

    

    

    

    Quadratic expression  can be factored:

  

  Again, the answer is: 6.82548584904245, -7.32548584904245.
Here's your graph:



  

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