322 NEW SERIES for the 
y x ; 
‘r—r y Sat 
r—tI 
and hence, multiplying by 2, and dividing by m, 
2 } Z 
=| BN (rr) n(r" —1T) 
m 2" m(r—t) m S50 Ga cae 
But 7? =x, and 7"= 4, (Art. §1.), from which it follows, that - 
T 
nm 
ry =x, andr=b" ; moreover, = = log «; therefore, fubftitu- 
ting, we get 
n (as) oon (x — 1) 
, logx <b”. ey 
a gee r) 
I 
logx > —. 
x”  m(b —t1r) 
and in thefe expreflions » denotes any whole, pofitive number 
whatever. 
55. By fubtracting the leffer of thefe limits to the logarithm 
of x from the greater, we find their difference tobe 
n («" —tI) ests 
x (o" a ae I) 
1 
(o" =1) 
Now 
zyx [4 
x m 
a 
