Question 743632

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


{{{log (x )/log(10)+ log(x+1)/log(10)=2}}}


{{{(log (x )+ log(x+1))/log(10)=2}}}


{{{(log(x(x+1)))/log(10)=2}}}


{{{log (x(x+1))=2*log(10)}}}


{{{log (x(x+1))=log(10^2)}}}


{{{log (x(x+1))=log(100)}}}


{{{x(x+1)=100}}}


{{{x^2+x=100}}}


{{{x^2+x-100=0}}}


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


{{{x = (-1 +- sqrt( 1^2-4*1*(-100) ))/(2*1) }}}


{{{x = (-1 +- sqrt( 1+400) ))/2 }}}


{{{x = (-1 +- sqrt( 401) ))/2 }}}


{{{x = (-1 +- 20.025 )/2 }}}


solution:


{{{x = (-1 + 20.025 )/2 }}}

{{{x = 19.025/2 }}}

{{{x = 9.5125 }}}....since we are dealing with logarithm, we need just positive solution