How to determine all real values of a if the equation 2lg(x-1)=lg(ax-3) has a single real solution?

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The equation 2*lg(x-1) = lg (ax-3) has two equal roots.

2*lg(x-1) = lg (ax-3)

=> lg ( x-1)^2 = lg (ax - 3)

taking the antilog of both the sides

=> (x -...

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