Lg(x-1)+lg(x+1)= 3lg2+lg(x-2)

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First, we can simplify the left side of the equation using logarithmic properties:

lg((x-1)(x+1)) = 3lg2 + lg(x-2)

Next, we can simplify the logarithm on the right side:

lg(x^2 - 1) = 3lg2 + lg(x-2)

Now, we can use the basic properties of logarithms to rewrite the equation:

lg(x^2 - 1) = lg(8) + lg(x-2)

Since the logarithms are equal, we can set the arguments equal to each other:

x^2 - 1 = 8(x-2)

Expanding the right side, we get:

x^2 - 1 = 8x - 16

Moving all terms to the left side:

x^2 - 8x - 15 = 0

Now we have a quadratic equation that we can solve by factoring or using the quadratic formula:

(x-5)(x-3) = 0

So the solutions to the equation are:

x = 5 or x = 3

Therefore, the values of x that satisfy the equation are x = 5 or x = 3.