Question 737009
log(x) + log(x+6) = 3


log[(x)*(x+6)] = 3


x(x+6) = 10^3


x(x+6) = 1000


x^2+6x = 1000


x^2+6x-1000 = 0



Use the quadratic formula to solve for x


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


{{{x = (-(6)+-sqrt((6)^2-4(1)(-1000)))/(2(1))}}} Plug in {{{a = 1}}}, {{{b = 6}}}, {{{c = -1000}}}


{{{x = (-6+-sqrt(36-(-4000)))/(2)}}}


{{{x = (-6+-sqrt(36+4000))/(2)}}}


{{{x = (-6+-sqrt(4036))/2}}}


{{{x = (-6+sqrt(4036))/2}}} or {{{x = (-6-sqrt(4036))/2}}}


{{{x = (-6+2*sqrt(1009))/2}}} or {{{x = (-6-2*sqrt(1009))/2}}}


<font color="red">Exact Solutions</font>: {{{x = -3+sqrt(1009)}}} or {{{x = -3-sqrt(1009)}}}


<font color="blue">Approximate Solutions</font>: {{{x = 28.764760}}} or {{{x = -34.764760}}}