Exponential inequalities

[parisse]

The solver can solve polynomial-like equations/inequations. Unfortunately there is no easy way to reduce all equations/inequations to a polynomial. But most of the time, you can help the CAS by calling the right pre-simplification command. Here you can do
a:=tsimplify(2^(3*x-1)+2^(6*x-2)-2^(3*x+3)-(4^(3*x-2))
This will express the inequation in terms of the minimum possible independant "variables", here 1, hence the inequation becomes polynomial-like, then
solve(a<0)
will return the exact answer.
The approx answer is partially wrong because the floats are too small for x negative.
Remember: the calc computes very fast but it is stupid, humans do not compute fast but humans know what to do, a typical situation where both can cooperate!