x = -8 and x = 2
To find this, follow these steps:
Since it's addition with the same log base, you need to multiply the two together:
x multiplied with x + 6 which produces x^2 + 6x
This then leaves you with:
logbase 4 (x^2 + 6x) = 2
To get rid of the log base, you need to use the base given (4) and set it to the power of 2 due to the fact that that is what is on the opposing side.
X^2 + 6x = 4^2
x^2 + 6x = 16
Now make this into a quadratic and solve for the roots:
x^2 + 6x - 16
(x + 8) (x - 2)
x = -8 and x = 2
Hope this helps!
