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

18
Iv.
Shew the truth of the following equivalents respectively:1. logl,(l + 2 + 3) =log1ol + logo2 + logo3.
2. 7. log,,-1- - 5 log + 3. logo-| =log,12.
3. 7. logo I + 6.1ogo0-} + 5. log, j- + logi0- = -logo13.
4. 16. logo,,1- + 12. logic2 + 7. log-So - log,15.
V.
Prove the truth of the following expressions and find the logarithms of each. Log0139= 2-1430148.
1. log1()l1 = 1 {log,,2 -log103}.
2. log,,(0)3= -{2 log,03 + log,,7-loglo2-1}.
3. iog1o(-i->)- = -{log1o23 - logo03 -log1o0139}.
4. log 10.(045) = {2 + 4 logo3 - 14 logo2}.
(720)
5. log10{(32) x ( 2 ) 1}2- {19lg02 - 14 log,o3;.
2(27)-l
6. log1c{ {3(602-1 5)60} {1 + 2(log,3-logo2)}.
{(60 + 15) x (16 x 9 )-}
7. lglO {5{21X12 } = — 1-{4 +' 7 og10g2l}.
10l x 23- -
VI.
Find the numerical values of x in each of the following equations,
having given log102, logi03, and logo17:5x=20: 100x=2: 8 = 100: 25x =800: 87x+1. 26+3 =54+3.203x+2:
3x=15:12x=180: 23x. 32 = 10: 152X =24x+1: 10x=102:
2x+5 +- 2. 2x+4= 212: 8.. 1252-X = 24x+3. 5x: 51-4 = 24x+1.
VII.
Solve the following equations:aC - ld = 0: mx = b - C-1 n. b =: a. b~ == c: mx-..-. x=?^:
a. Cn = b-n a:.+2. b x+3 = xO-. x-5: 22+1-(2-1)-1 = 0:
(a + + )2(a4- + -2 4)x- (a - )2X' 21 = bX-21:
{a + b2m a + b b)2x a x1 =b
{ c = { C f ''-_(ox + do).
VIII.
Find the values of x and y in each of the following sets of equations:a'by '- p amx. bny=gr, =:x. dY =s,.:: a +y b, b:: —:
x+y= 2, -, x +. v: X.+y _=X by = 1x^ a^^n. 2 _ ^,. = lg'
(xy)lo (yX)loGc _ a+ -,logy: X Y- a X =by.
( x), (ey)Iogc, Cl00'x aOY y=.x xrnz= y4