Question 629966
log(x-30)=3-logx


{{{10^log(x-30) = 10^(3-log(x))}}}  (make both Side Exponents of 10)


{{{10^log(x-30) = (10^3)/(10^log(x))}}}   (10^(a-b) = 10^a/10^b)


{{{(x-30) = 1000/x}}}   (simplify 10^log(a) = a)


{{{x^2-30*x = 1000}}}  (multiply both sides by x)


{{{x^2 -30x -1000 = 0}}}  (subtract 1000 from both sides)


{{{(x-50)*(x+20) = 0}}}   (Factor quadratic)


Either (x-50) = 0 or (x+20) = 0


x = 50 or x = -20 (solve)


However, x = -20 is an invalid solution as you can's take the log of a negative number.


x = 50 (answer)