Question 919449
solve for x: log(x + 9) = 1 - log(x - 8)
log(x+9)=1-log(x-8)
log(x+9)+log(x-8)=1
log((x+9)(x-8))=1
(x+9)(x-8)=10 (base(10) raised to log of number(1)=number(x+9)(x-8))
x^2+x-72=10
x^2+x-82=0
solve for x by quadratic formula:
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
a=1, b=1, c=-82
{{{x = (-1 +- sqrt( 1-4*1*-82 ))/(2*1) }}}
{{{x = (-1 +- sqrt( 1+328))/(2) }}}
{{{x = (-1 +- sqrt( 329))/(2) }}}
x=(√(329)-1)/2≈8.56 (Ignore negative root)