Question 919205

 

{{{log((x + 3)) = 1 - log((x - 2))}}}

{{{log((x + 3))+ log((x - 2))= 1 }}}

{{{log((x + 3)(x - 2))= 1}}} ...........{{{log(10,10)=1}}}

{{{log((x + 3)(x - 2))=log(10)}}}  if log same, then

{{{(x + 3)(x - 2)= 10}}}

{{{x^2-2x + 3x - 6= 10}}}

{{{x^2 + x - 6-10=0}}}

{{{x^2 + x - 16=0}}} .......use quadratic formula to solve for {{{x}}}


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

{{{x = (-1 +- sqrt( 1^2-4*1*(-16) ))/(2*1) }}} 

{{{x = (-1 +- sqrt( 1+64 ))/2 }}} 

{{{x = (-1 +- sqrt( 65 ))/2 }}}

{{{x = (1/2)(-1 +- sqrt( 65 )) }}}

solutions:

{{{x = (1/2) (-1-sqrt(65)) }}}

{{{x = (1/2 )(-1-8.06)}}} 

{{{x = (1/2) (-9.06)}}} 

{{{x =-4.53 }}} 


or 

{{{x = (1/2) (sqrt(65)-1)}}}

{{{x =( 1/2 )(8.06-1)}}}

{{{x = (1/2) (7.06)}}}

{{{x =3.53}}}