Question 996322


{{{log(sqrt(3),(1-x)^2) - log(sqrt(3), (3-x)) < 2}}}


{{{log(sqrt(3),(1-x)^2/ (3-x)) < 2}}}...........change to base {{{10}}}

{{{log((1-x)^2/ (3-x))/log(sqrt(3)) < 2}}}

{{{log((1-x)^2/ (3-x)) < 2log(sqrt(3))}}}

{{{log((1-x)^2/ (3-x)) < log((sqrt(3))^2)}}}

{{{log((1-x)^2/ (3-x)) < log(3)}}}....if log same, then

{{{(1-x)^2/ (3-x) < 3}}}......solve for {{{x}}}

{{{(1-x)^2 < 3(3-x)}}}

{{{1-2x+x^2 < 9-3x}}}

{{{1-2x+x^2-9+3x<0}}}

{{{x^2+x-8<0}}}.....use quadratic formula

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

{{{x = (-1 +- sqrt( 1^2-4*1*(-8) ))/(2*1) }}}

{{{x = (-1 +- sqrt( 1+32 ))/2 }}}

{{{x = (-1 +- sqrt( 33 ))/2 }}}

 exact solutions:

{{{x = (1/2)(-1 + sqrt( 33 )) }}}

{{{x = (1/2)(-1 - sqrt( 33 )) }}}