Solve log equations problem [SageMath]

Question

Input

var('x')
solve((log((x**2 - x), 6) - log((6*x - 10), 6) == 0), x)

Output

[log(x^2 - x) == log(6*x - 10)]

But real roots are 5 and 2. What I doing wrong?

Answer 1

You need to use the option to_poly_solve=True which have the following semantic:

to_poly_solve- bool (default: False); use Maxima's to_poly_solverpackage to search for more possible solutions, but possibly encounter approximate solutions. This keyword is incompatible withmultiplicities=True``.

So,

solve(..., x, to_poly_solve=True)

should do.