Question 747856

{{{log (x) + log(3x+5)=1}}}...it is base {{{10}}} log

{{{(log (x) + log(3x+5))/log(10)=1}}}

{{{log (x(3x+5))=1*log(10)}}}

{{{log (x(3x+5))=log(10)}}}

{{{x(3x+5)=10}}}

{{{3x^2+5x=10}}}

{{{3x^2+5x-10=0}}}....use quadratic formula


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


{{{x = (-5 +- sqrt( 5^2-4*3*(-10) ))/(2*3) }}}


{{{x = (-5 +- sqrt( 25+120 ))/6 }}}


{{{x = (-5 +- sqrt( 145 ))/6 }}}


{{{x = (-5 +- 12.042)/6 }}}

solutions:

{{{x = (-5 +12.042)/6 }}}

{{{x = 7.042/6 }}}

{{{highlight(x = 1.174) }}}

since logarithm of negative number {{{unidentified}}}, we will use only 

positive solution {{{highlight(x = 1.174) }}}