1889 - 90 .] Lord M'Laren on Equation of n ill Degree. 
277 
Thus the value of the equation resulting from the value found 
for x is correct within the limits of accuracy attainable in logarithmic 
computation. 
Solution of the Three- Term Equation of the n th degree. 
cux n ± (3x n ~ p . 
I. Where the two terms of x are both positive , we have the two 
forms corresponding respectively to 
, , , f =log(aX n ) + \oy™ ) 
log {«*” + /&-}={ =log(/&-) + Xo yr 4 
Case (1). Log {ax n + /3x n ~ p ] = 0 = log a + n log x + \oy n n _ p ; 
... -w = x °y"-* +1 °g a .... 
Also log (oaf) - log (/ 3x n p ) = vcC_ p ; 
- log £ = log a - log p - C, • • 
Equating (1) and (2), 
P hoy n n _ p +p log a = n log a - n log /3 - nV(C-p \ 
' n -p s 
whence 
mIU+ 
(fK,-c 
loga-log/3 = ? 
( 1 ). 
( 2 ). 
(A) 
For the indices n and (n — 1), this becomes 
m:-. + ©wu, =(^) M } < A .>- 
Case (2). Where /3x n ~ p is the greater of the two terms , in the 
positive equation, 
log { ocx n + px n - p } = 0 = log p + (n -p) log X + \oy n p - p ; 
( 1 ). 
- log X = 
Also 
- log X = 
whence, 
mr p -( 
Voy; 
K n -pj 
(n-p) 
l~ p + \og( 
p 
For the indices n and (n- 1) this becomes 
1 
( 2 ). 
m 
n-p 
— r hoy n n - 1 = log log CL . . . (Bj) . 
— l n i 
