1 | initial version |

Looks like you found a typo in the Sage code that is raising that exception. I'll start a ticket for that. Thanks.

It is probably the case that without changing some settings/assumptions in Maxima directly, it's not going to be able to solve your particular equation. The assumptions you need relating `x`

and `k`

are tricky.. you have fractional exponents depending on `k`

, so you've got to assume `x`

is real and positive. But doing that doesn't seem to help Maxima.

Here is a work around, though. If you know the form of the equation is going to be like the one you have, the human mathematician would probably take the `log`

of both sides and solve for `log(x)`

, then exponentiate. This kind of process is easy to automate:

```
sage: var('x,y,k')
sage: eq = (1/(x^((k - 2)/k))) == 1/2*(k + 1)*x^(1/k)
sage: eq = log(eq)
sage: eq.full_simplify()
-(k - 2)*log(x)/k == -(k*log(2/(k + 1)) - log(x))/k
sage: eq = eq.full_simplify()
sage: eq = eq.subs(log(x) == y)
sage: solve(eq, y)
[y == k*log(2/(k + 1))/(k - 1)]
sage: S = solve(eq, y)
sage: soln = exp(S[0].rhs())
sage: soln
e^(k*log(2/(k + 1))/(k - 1))
```

2 | No.2 Revision |

Looks like you found a typo in the Sage code that is raising that exception. I'll start a ticket for that. Thanks.

It is probably the case that without changing some settings/assumptions in Maxima directly, it's not going to be able to solve your particular equation. The assumptions you need relating `x`

and `k`

are tricky.. you have fractional exponents depending on `k`

, so you've got to assume `x`

is real and positive. But doing that doesn't seem to help Maxima.

Here is a work around, though. If you know the form of the equation is going to be like the one you have, the human mathematician would probably take the `log`

of both sides and solve for `log(x)`

, then exponentiate. This kind of process is easy to automate:

```
sage: var('x,y,k')
sage: eq = (1/(x^((k - 2)/k))) == 1/2*(k + 1)*x^(1/k)
sage: eq = log(eq)
sage: eq.full_simplify()
-(k - 2)*log(x)/k == -(k*log(2/(k + 1)) - log(x))/k
sage: eq = eq.full_simplify()
sage: eq = eq.subs(log(x) == y)
sage: solve(eq, y)
[y == k*log(2/(k + 1))/(k - 1)]
sage: S = solve(eq, y)
sage: soln = exp(S[0].rhs())
sage: soln
e^(k*log(2/(k + 1))/(k - 1))
```

Hopefully there is a better answer which involves telling Maxima to load a package for doing "logarithmic solving" or whatever the process I just described is called.

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