With HP50G,approx mode (but exact mode is OK):
Code:

`'SIN(X)=COS(X)' SOLVEVX `

{ X 'LN(X)'} Lsub

{ n1 n n2 n } Lsub

SOLVEVX

here,you get :

Code:

`{ 'X=EXP(6.2832*n-2.3562)' `

'X=EXP(6.2832*n+0.7854)' }

Then you can test with some n values

Note that Lsub is a program I use for | (or SUBST) when equations are in a list (list processing don't work with | or subst) :

Code:

`« 1 ->LIST { | } + ->PRG MAP »`

I also often use Lexr to get only the right part of equations in a list :

Code:

`« 1 « EXLR NIP » DOSUBS »`

Ex :

{ 'X=EXP(6.2832*n-2.3562)'

'X=EXP(6.2832*n+0.7854)' }

Lexr

gives

{ 'EXP(6.2832*n-2.3562)' 'EXP(6.2832*n+0.7854)' }

and for example to test n from -5 to 5, continue with

STEQ {}

-5 5 FOR a

EQ 'n' a 2 ->LIST Lsub +

NEXT

XNUM SORT

that gives

{ 2.1526E-15 4.9812E-14 1.1527E-12 2.6674E-11 6.1725E-10 1.4284E-8 3.3053E-7 7.6487E-6 0.0002

0.0041 0.0948 2.1933 50.7540 1174.4832 27178.3539 628925.9347 14553781.7413 336784589.923 7793428678.94 180345337617. 4.1733E12 9.6573E13 }

In exact mode you get

{ 'EXP(2*ATAN(-1+√2)-2*PI)' '1/EXP(2*ATAN(1+√2))' 'EXP(2*ATAN(-1+√2))' }

As you see the HP don't simplify the ATAN (but you can write easily your own program for trivial trig simplifications with a serie of MATCH commands. But it's not automatic and rather slow). I can post this if there is some intesrest

with the Prime
solve(sin(ln(x))=cos(ln(x)))

returns directly the symbolic simplified general solution... ( 'principal' uncheck in CAS setting)

It would fine if we could do :

equation | n={-1,0,1,2}

or

equation | n={-5...5}

to obtain a list of equations for each value.

But this dont work ....

So I do this:

Edit the general solution to change n_xxx by n

then

f(n):=ANS

concat(f(-1),f(0))

concat(ANS,f(1))

concat(ANS,f(2))

sort(ans)

~=

and you get the result (approx or exact)