Elementary arithmetic, with brief notices of its history... by Robert Potts.

19
IX.
Determine the values of x, y,, in the following equations -
1. a. Y. yZ=C, Y. 3Z. ^. = b, a.. y/ c.
2. ax. +bYZ= 0C aly. blx+ =,13 a 72Z. 25x+= 2
3. y10. ogy, O. o = a2, xloy. ylog, =X Y.
X.
Find the values of the unknown quantity in each of the quadratic
equations:M + bax + c=0 a+ aC-X= c ax + ax = 6a3: ax- 8a- = 2:
+ =2: a bX-PO 7x=O: 4 =oeX -XO
ax loga x )
42x-8.4x + 7=0: 32x + 3"= 4785156: 4X+2 + 16 — 5120:
10 — 60.10 — 4=0: 52x= 100.5X-3 + 5 -1: 27(3x+-32x+3) = 2:
32- 2.3x+ = 567: 22x- 100.2x + 1 14336: 3~+4- 3'+6 = 2
/ og + x a a } = b: logo{ 1 - }=2 '+ X (G-_)_2
N/(as + x — a 1 q- N/} --- ~
61 v9+zo-hb ^1+/- X/ 1-21-e'2
XI.
1. Prove that x' is greater than e, and 2x less than e, when x is
any positive integer greater than 2.
2. If x and y be positive, prove that xJ is less than yx when x is
greater than y, and y greater than e: but y is greater than y' when
x is greater than y, and y less than e.
3. Solve the equation x"= 100 by approximation to three places of
decimals.
4. Find x and y ini whole numbers from the equation xy = x.
5. Solve the equations xy= 500 and y= 300, by approximation.
6. Find the values of in each of the four following equations:aex ear = a a 6c = -: (log' ( = loO~.'e'
7. Express the equation m(loga+x) nlogex+l in an exponental
form.
8. Find x and y in the three following sets of equations:2^x=512, 2y=256: (22 )2y=1 16, { }Y = 3: (4x)y'=16, 3. 9 =27.
9. Shew whether log{log,025} is equivalent to log0o{log,25}.
10. Find xx from X3 —21X2 +147x-316 = 0.
XII.
1. If y -=, a n and x anc loggy be in harmonical progression, find
the values of x and y.
2. Given log83 = %n, and 1og,24 = n; find log1045.
loge + a logox -
3. Find logx from the equation logex logl^
loglo0 log'X
4. In the equationlg- I +- - + 1 logo2 = (2-4(logl 0 - 1) 1
l1ogoX 4 logeX (2 0gl- 1)2l —I