excelsolverexponentialexponent

How do I use Excel Solver for exponents?

My equation is Q^Q^.25=6,512,786

I have the following input

enter image description here

And here is my solver enter image description here

I keep getting errors.

Solution

  • The problem is with the non-standard way that Excel handles iterated exponents. Excel parses Q^Q^0.25 as (Q^Q)^0.25, which grows very rapidly. You probably intended Q^(Q^0.25), which, while still growing rapidly, doesn't explode in the same way. If you change your equation in D2 to

    =C2^(C2^0.25)

    and rerun the solver with the same settings (but a nonzero starting value at C2 since 0^0 is undefined) you will get convergence, to approximately 117.44.

    On Edit: It turns out that in the programming world there is a greater diversity of how associativity of exponentiation is handled than I realized. This answer to a related question contains an interesting table surveying how different programming languages handle it.