Question 805669
{{{log(x + 3) = log( 4)- log(2x -3)}}}



{{{log(x + 3) = log( 4/(2x -3))}}}.....if log same, than


{{{ x + 3 = 4/(2x -3)}}}........solve for {{{x}}}


{{{ (x + 3)(2x -3) = 4}}}


{{{  2x^2 -3x+6x-9 = 4}}}


{{{  2x^2 +3x-9 -4=0}}}


{{{  2x^2 +3x-13=0}}}


{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 


{{{x = (-3 +- sqrt( 3^2-4*2*(-13) ))/(2*2) }}} 


{{{x = (-3 +- sqrt( 9+104 ))/4 }}} 

{{{x = (-3 +- sqrt( 113 ))/4 }}} 


 

solutions:

{{{x = (-3 + sqrt( 113 ))/4 }}} or

{{{x = (  sqrt( 113 )-3)/4 }}}

{{{x = (1/4) (sqrt(113)-3)}}}


{{{x = 1.907536453183662351999780478732328555491816064645649120199218  }}} ...round it 

{{{x = 1.9 }}} ......your solution


or

{{{x = (1/4) (-sqrt(113)-3)}}} but we have log and we do not need negative solution