Answer:
x=2
Explanation:
We can use the product rule of logarithms to simplify the equation:
㏒(x+3)+㏒x = 1
㏒[(x+3)x] = 1
(x+3)x = 10
Expanding the left side and rearranging the equation, we get:
x^2 + 3x - 10 = 0
We can now use the quadratic formula to solve for x:
x = (-b ± √(b^2 - 4ac)) / 2a
Where a = 1, b = 3, and c = -10
x = (-3 ± √(3^2 - 4(1)(-10))) / 2(1)
x = (-3 ± √49) / 2
x = (-3 ± 7) / 2
So x can be equal to -5 or 2. We need to check which solution, if any, is extraneous by plugging each one into the original equation and verifying that it is valid:
㏒(-5+3)+㏒(-5) ≠ 1
㏒(2+3)+㏒(2) = 1
Therefore, the solution to the equation is x = 2.