Lg(x-1)+lg(x-3)=lg(3/2 x-3)

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To solve this equation, we can first combine the logarithms on the left side using the product rule of logarithms:

lg(x-1)+lg(x-3) = lg((x-1)(x-3))

Now we have:

lg((x-1)(x-3)) = lg(3/2 x-3)

Now we can drop the logarithm on both sides and solve for x:

(x-1)(x-3) = 3/2 x - 3
x^2 - 4x + 3 = 3/2 x - 3
2x^2 - 8x + 6 = 3x - 6
2x^2 - 11x + 12 = 0

Now we can factor the quadratic equation:

(2x-3)(x-4) = 0

Setting each factor to zero, we get:

2x - 3 = 0 or x - 4 = 0

Solving for x:

2x = 3 or x = 4

Therefore, the solutions to the equation lg(x-1)+lg(x-3) = lg(3/2 x-3) are x = 3/2 or x =4.