Cambridge Additional Mathematics

Surds, indices, and exponentials (Chapter 4) 117

EXERCISE 4F

1 Solve forx:

a 2 x=8 b 5 x=25 c 3 x=81 d 7 x=1

e 3 x=^13 f 2 x=

p

2 g 5 x= 1251 h 4 x+1=64

i 2 x¡^2 = 321 j 3 x+1= 271 k 7 x+1= 343 l 51 ¡^2 x=^15

2 Solve forx:

a 8 x=32 b 4 x=^18 c 9 x= 271 d 25 x=^15

e 27 x=^19 f 16 x= 321 g 4 x+2= 128 h 251 ¡x= 1251

i 44 x¡^1 =^12 j 9 x¡^3 =27 k (^12 )x+1=8 l (^13 )x+2=9

m 81 x=27¡x n (^14 )^1 ¡x=32 o (^17 )x=49 p (^13 )x+1= 243

3 Solve forx, if possible:

a 42 x+1=8^1 ¡x b 92 ¡x=(^13 )^2 x+1 c 2 x£ 81 ¡x=^14

4 Solve forx:

a

32 x+1

3 x

=9x b

25 x

5 x+4

=25^1 ¡x c

4 x

2 x+2

=

2 x+1

8 x

d

52 x¡^5

125 x

=

251 ¡^2 x

5 x+2

e

4 x

82 ¡x

=2x£ 4 x¡^1 f

92 x

272 ¡x

=

813 x+1

31 ¡^2 x

5 Solve forx:

a 3 £ 2 x=24 b 7 £ 2 x=28 c 3 £ 2 x+1=24

d 12 £ 3 ¡x=^43 e 4 £(^13 )x=36 f 5 £(^12 )x=20

Example 24 Self Tutor

Solve forx: 4 x+2x¡20 = 0

4 x+2x¡20 = 0

) (2x)^2 +2x¡20 = 0 fcompare a^2 +a¡20 = 0g

) (2x¡4)(2x+5)=0 fa^2 +a¡20 = (a¡4)(a+5)g

) 2 x=4or 2 x=¡ 5

) 2 x=2^2 f 2 xcannot be negativeg

) x=2

6 Solve forx:

a 4 x¡6(2x)+8=0 b 4 x¡ 2 x¡2=0 c 9 x¡12(3x)+27=0

d 9 x=3x+6 e 25 x¡23(5x)¡50 = 0 f 49 x+ 1 = 2(7x)

4037 Cambridge

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Y:\HAESE\CAM4037\CamAdd_04\117CamAdd_04.cdr Tuesday, 14 January 2014 2:28:46 PM BRIAN