Question 738480
{{{log ((x)) + log((x + 48)) = 2}}}....in base {{{10}}} you will have


{{{log ((x))/log ((10)) + log((x + 48))/log ((10)) = 2}}}


{{{(log ((x)) + log((x + 48)))/log ((10)) = 2}}}


{{{log ((x)) + log((x + 48)) = 2log ((10))}}}

{{{log (x(x + 48)) = log ((10^2))}}}

{{{log ((x^2 + 48x)) = log ((100))}}}

{{{x^2 + 48x = 100}}}

{{{x^2 + 48x -100=0}}}...use quadratic formula

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

{{{x = (-48 +- sqrt( 48^2-4*1*(-100) ))/(2*1) }}}

{{{x = (-48 +- sqrt( 2304+400 ))/2 }}}

{{{x = (-48 +- sqrt( 2704 ))/2 }}}

{{{x = (-48 +- 52)/2 }}}

solutions: we need only positive solution

{{{x = (-48 + 52)/2 }}}

{{{x = 4/2 }}}

{{{highlight(x = 2) }}}