LN X:

	 10 	REM DEMONSTRATION FOR LN X
	 20 	REM USING THE 'SERIES GENERATOR'
	 30 	LET D=0	(This makes D the first variable).
	 40 	DIM A(12)
	 50 	LET A(1)= -.0000000003
	 60 	LET A(2)=0.0000000020
	 70 	LET A(3)= -.0000000127
	 80 	LET A(4)=-0.0000000823
	 90 	LET A(5)= -.0000005389
	100 	LET A(6)=0.0000035828
	110 	LET A(7)= -.0000243013
	120 	LET A(8)=0.0001693953
	130 	LET A(9)= -.0012282837
	140 	LET A(10)=0.0094766116
	150 	LET A(11)= -.0818414567
	160 	LET A(12)=0.9302292213
	170 	PRINT
	180 	PRINT "ENTER START VALUE"
	190 	INPUT C
	200 	CLS
	210 	PRINT "BASIC PROGRAM", "ROM PROGRAM"
	220 	PRINT "-------------", "-----------"
	230 	PRINT
	240 	LET C=SQR C
	250 	FOR J=1 TO 4
	260 	LET C=C*C
	270 	IF C=0 THEN STOP 	(STOP with 'invalid argument'.)
	280 	LET D=C
	290 	LET V=PEEK 23627+256*PEEK 23628+1
	300 	LET N=PEEK V-128	(N holds e').
	310 	POKE V,128
	320 	IF D<=0.8 THEN GO TO 360	(D holds X').
	330 	LET S=D-1
	340 	LET Z=2.5*D-3
	350 	GO TO 390
	360 	LET N=N-1
	370 	LET S=2*D-1
	380 	LET Z=5*D-3
	390 	LET R=N*0.6931471806	(R holds N*LN 2).
	400 	LET BREG=12
	410 	REM USE 'SERIES GENERATOR'
	420 	GO SUB 550
	430 	PRINT TAB 8;"LN ";C
	440 	PRINT
	450 	PRINT S*T+R,LN C
	460 	PRINT
	470 	NEXT J
	480 	GO TO 170

NOTES:

  i. When C is entered this program calculates and prints LN C, LN (C**2), LN (C**4)
     and LN (C**8). It also prints the values obtained by using the ROM program.
     For a specimen of results, try entering these values: 1.1; 0.9; 300; 0.004; 1E5 (for
     overflow) and 1E-5 (STOP as 'invalid argument').

 ii. The constants A(1) to A(12) in lines 50 to 160 can be obtained by integrating 5*LN
     (4* (X+1)/5)/(4*X-1) over the interval U=0 to PI, after first multiplying by COS
     (N*U) for each constant (i.e. for N=1,2,...,12) and substituting COS U=2*X-1. Each
     result should then be divided by PI.