solve for solutions (x) // log (x-3)= -logx+1

Answer 1

log(x - 3) = - logx + 1; because 1 = log10, we have log(x - 3) = log10 - logx, or x - 3 = 10/x and we get quadratic equation: x² - 3x - 10 = 0, (x - 5)(x + 2) = 0, x - 5 = 0 or x + 2 = 0. x = 5 or x = - 2.

x = - 2 not in domain of equation: x > 3. So solution is only x = 5.