Question 966659
log(x^2 + 7x) = log(18) can only be true if x^2 + 7x = 18


so, start with x^2 + 7x = 18.


subtract 18 from both sides of the equation to get x^2 + 7x - 18 = 0


factor this quadratic equation to get (x + 9) * (x - 2) = 0


solve for x to get x = -9 or x = 2.


go back to your original equation to see if these values are good.


they have to be good in the original equation, or they are not good.


your original equation is log(x^2 + 7x) = log(18)


when x = -9, you get log(x^2 + 7x) = log(18) becomes log(81 - 63) = log(18) which becomes log(18) = log(18) which is true, so x = -9 is good.


when x = 2, you get log(x^2 + 7x) = log(18) becomes log(4 + 14) = log(18) which becomes log(18) = log(18) which is true, so x = 2 is also good.


your solution is that x = -9 or x = 2.