To solve this equation, we can use the properties of logarithms.
First, combine the two logarithms using the property that lg(a) + lg(b) = lg(ab):
lg[(2-x)(1-x)] = lg(12)
Next, simplify the expression inside the logarithm:
(2-x)(1-x) = 12 - 2x - x + x^2 = 1x^2 - 3x - 10 = 0
Now we have a quadratic equation. We can solve this equation by factoring:
(x-5)(x+2) = 0
Setting each factor equal to zero gives us the solutions:
x-5 = 0 or x+2 = x = 5 or x = -2
Therefore, the solutions to the equation lg(2-x) + lg(1-x) = lg(12) are x = 5 and x = -2.
To solve this equation, we can use the properties of logarithms.
First, combine the two logarithms using the property that lg(a) + lg(b) = lg(ab):
lg[(2-x)(1-x)] = lg(12)
Next, simplify the expression inside the logarithm:
(2-x)(1-x) = 1
2 - 2x - x + x^2 = 1
x^2 - 3x - 10 = 0
Now we have a quadratic equation. We can solve this equation by factoring:
(x-5)(x+2) = 0
Setting each factor equal to zero gives us the solutions:
x-5 = 0 or x+2 =
x = 5 or x = -2
Therefore, the solutions to the equation lg(2-x) + lg(1-x) = lg(12) are x = 5 and x = -2.