Business Mathematics - Theory of Indices

 

Business Mathematics

Theory of Indices

 

CONTENTS:

1.   Formulas

2.   12 Selected Problems

3.   Solutions to the Selected

    Problems

 

Formulas

1	(am × an) =	a(m + n)
2	(am ÷ an) =	a(m – n)
3	(am)n =	amn
4	(ab)m =	am × bm
5	a(−n) =	1/(an)
6	n√a =	a(1/n)
7	a0	1
8	(abc...)m =	am × bm × cm.......
9	(a/b)m =	(am/bm)
10	(am × bm × cm...)n =	amn × bmn ×cmn
11	n√am	a(m/n)
12	If am = bm,	a = b
13	If am = an,	m = n

 

Theory of Indices

Selected Problems

 

1	Express the following in single positive index: [x(−3/4)]5/3
2	Simplify [{(81)n.35 – 3(4n – 1).243}/92n.33] – [4.3n/{3(n + 1) – 3n}]
3	Show that (xb/xc)a × (xc/xa)b × (xa/xb)c = 1
4	Show that (xm/xn)m+n−l × (xn/xl)n+l−m × (xl/xm)l+m−n = 1
5	Show that [x(a^2 + b^2)/x−ab]a−b × [x(b^2 + c^2)/x−bc]b−c × [x(c^2 + a^2)/x−ca]c−a = 1
6	Show that [1/(1 + xb−a + xc−a)] + [1/(1 + xa−b + xc−b)] + [1/(1 + xa−c + xb−c)] = 1
7	If 2x = 3y = 6z, show that z = (xy)/(x + y)
8	If ax = by = cz and b2 = ac, prove that (1/x) + (1/z) = (2/y)
9	If xa = yb = (xy)c, show that ab = c(a + b)
10	Show that x3 – 6x – 6 = 0, if x = 3√2 + 3√4
11	Solve (√5)(4x – 4) – 5(2x – 3) = 20
12	Solve 2(x + 3) + 2(x + 1) = 320

 

Click here for the Solutions to Selected Problems in PDF