07 Nov Solving the exponent of exponent expression on the HP15C or DM15L

Solving the equation below on a modern CAS or RPN calculator is quite easy, but doing it on the older HP15C or the latest DM15L is a little different. On an HP35s or HP Prime, even the HP50C enter the equation into the equation writer or solver, then solve for ‘x’ without thinking much. On the other hand the HP15C forces you to understand the flow of calculations and their relation to each other. In my opinion, a fundamental aspect missing in today’s math’s education.

\(\\[20px]\Large x^{x^2}=256\)

I posted this because I got it wrong and forgot the rules of exponents. A lot of people start from the bottom and work upwards to ‘x’, while the correct way is working from ‘x’ down to 2. So

\(\\[20px]\Large (x^x)^2 \ne x^{(x^2)} \)

Below is the program you can enter on the HP15C or DM15L (I assume the HP11C will work the same, even the venerable HP41 range, albeit with some changes in key selection.

[f][PGRM]
[g][P/R]
[F][LBL][C]
[2]
[yx]
[yx]
[2][5][6]
[-]
[g][RTN]
[g][P/R]

To run the program, enter the following keys:

[1]

[ENTER] …. (Enter lower estimate)

[5] …. (Enter upper estimate and do not press [ENTER])

[f][SOLVE][C]

The answer should be 2, enjoy.