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I have no problems with 5:

sage: solve((log((x*2 - x), 6) - log((6x - 10), 6) == 0),

x,to_poly_solve=True)

[x == 2, x == 5]

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I have no problems with 5:

sage: solve((log((x*2 solve((log((x**2 - x), 6) - log((6x log((6*x - 10), 6) == 0), 

x,to_poly_solve=True)

[x == 2, x == 5]

5]