MATLAB: “Solve” Command Gives One Output

commandrealsolve

I entered:
solve('x^4 – 2^x = 0')
but it only displayed one of the three real answers:
ans =
-(4*lambertw(k, -((-1)^(l/2)*log(2))/4))/log(2)
How do I get all three answers?

Best Answer

That solution does not appear to be real-valued. The (-1)^(1/2) is the imaginary constant. That solution corresponds to the solution
-4*LambertW(-(1/4*I)*ln(2))/ln(2)
which is imaginary.
The three real-valued solutions are
-4*LambertW((1/4)*ln(2))/ln(2),
-4*LambertW(-(1/4)*ln(2))/ln(2),
-4*LambertW(-1, -(1/4)*ln(2))/ln(2)
I do not know, however, if there is a way to get MuPad to emit them.
I note that the solution you show has introduced a new undefined constant "k". Possibly the solutions correspond to different k.
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