In the maxima interface we are always converting floating-point numbers 
into exact fractions. This is why solve behaves in the way you describe.



On Tuesday, June 12, 2012 1:47:09 AM UTC+1, Eviatar wrote:
>
> solve has inconsistent behaviour when using exact numerical 
> representations of numbers.
>
> For example:
>
> sage: solve(sin(x) == 0.5, x)
> [x == 1/6*pi]
> sage: arcsin(0.5)
> 0.523598775598299
>
> sage: solve(log(x) == 0.5, x)
> [x == sqrt(e)]
> sage: e^0.5
> 1.64872127070013
>
> Shouldn't this be consistent? It seems to me that returning approximations 
> makes more sense, because that's what all the functions do.
>

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