Question

Which of the following shows the true solution to the logarithmic equation below?

log (x) + log (x + 5) = log (6 x + 12)
x = negative 3
x = 4
x = negative 3 and x = 4
x = negative 3 and x = negative 4

Answer 1

Combine the logs: log[x(x+5)] = log(6x+12) ⇒ x(x+5) = 6x+12 ⇒ x^2 - x -12 = 0 ⇒ x = 4 or x = −3.

But logs require x>0, so x = −3 is extraneous. The true solution is x = 4.