Lg(2-x)+lg(1-x)=lg(12)

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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
2 - 2x - x + x^2 = 12
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 = 0
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.