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exponents

Transcript of Exponents and Logarithms

• IB Questionbank Maths SL 1

Exponents And Logarithms

1. Solve the following equations.

(a) logx 49 = 2

(3)

(b) log2 8 = x

(2)

(c) log25 x =

(3)

(d) log2 x + log2(x 7) = 3

(5)

(Total 13 marks)

2. Solve the equation log9 81 + log9 + log9 3 = log9 x.

(Total 4 marks)

3. Solve the equation 43x1

= 1.5625 102.

(Total 4 marks)

2

1

9

1

• IB Questionbank Maths SL 2

4. Solve the equation 9x1

=

(Total 4 marks)

5. Let log10P = x , log10Q = y and log10R = z. Express in terms of x , y and z.

(Total 4 marks)

6. If loga 2 = x and loga 5 = y, find in terms of x and y, expressions for

(a) log2 5;

.31

2x

2

310log

QR

P

• IB Questionbank Maths SL 3

(b) loga 20.

(Total 4 marks)

7. Let ln a = p, ln b = q. Write the following expressions in terms of p and q.

(a) ln a3b

(b) ln

(Total 6 marks)

8. Solve the equation log27 x = 1 log27 (x 0.4).

(Total 6 marks)

b

a

• IB Questionbank Maths SL 4

9. (a) Given that log3 x log3 (x 5) = log3 A, express A in terms of x.

(b) Hence or otherwise, solve the equation log3 x log3 (x 5) = 1.

(Total 6 marks)

10. Given that log5 x = y, express each of the following in terms of y.

(a) log5 x2

(b) log5

(c) log25 x

x

1

• IB Questionbank Maths SL 5

(Total 6 marks)

11. Let a = log x, b = log y, and c = log z.

(Total 6 marks)

12. Let p = log10 x, q = log10 y and r = log10 z.

Write the expression log10 in terms of p, q and r.

(Total 6 marks)

13. Find the exact solution of the equation 92x

= 27(1x)

.

(Total 6 marks)

14. Solve log2x + log2(x 2) = 3, for x > 2.

3

2

z

yx

zy

x2

• IB Questionbank Maths SL 6

(Total 7 marks)

15. (a) Find log2 32.

(1)

(b) Given that log2 can be written as px + qy, find the value of p and of q.

(4)

(Total 5 marks)

16. (a) Let logc 3 = p and logc 5 = q. Find an expression in terms of p and q for

(i) log c 15;

(ii) log c 25.

(b) Find the value of d if log d 6 = .

(Total 6 marks)

y

x

8

32

2

1

• IB Questionbank Maths SL 7

17. Given that p = loga 5, q = loga 2, express the following in terms of p and/or q.

(a) loga 10

(b) loga 8

(c) loga 2.5

(Total 6 marks)

18. (a) Given that (2x)2 + (2

x) 12 can be written as (2x + a)(2x + b), where a, b , find the value of a and of b.

(b) Hence find the exact solution of the equation (2x)2 + (2

x) 12 = 0, and explain why there is only one solution.

(Total 6 marks)

• IB Questionbank Maths SL 8

EXTRA PRACTISE

19. Solve the following logarithmic equations

• IB Questionbank Maths SL 9

20. Solve the following logarithmic equations:

• IB Questionbank Maths SL 10

21. Solve the following logarithmic equations:

• IB Questionbank Maths SL 11

• IB Questionbank Maths SL 12

22. Solve the following equations, giving exact answers:

• IB Questionbank Maths SL 13

23. Solve the following equations, giving exact answers:

• IB Questionbank Maths SL 14

24. Solve the following simultaneous equations:

25. Solve the following equations:

• IB Questionbank Maths SL 15

• IB Questionbank Maths SL 16

26. Solve the following equations:

27. Solve the following equations (Hidden Quadratic Equations):

• IB Questionbank Maths SL 17

28.

• IB Questionbank Maths SL 18

29.

30.

• IB Questionbank Maths SL 19

• IB Questionbank Maths SL 20

31. Solve the following equations:

A.

B.

• IB Questionbank Maths SL 21

C.

D.

• IB Questionbank Maths SL 22

E.

F.

• IB Questionbank Maths SL 23

32. Write down the following equations without logarithms:

A.

B.

C.

D.

E.

F.

G.

H.

• IB Questionbank Maths SL 24

33. Evaluate the following (without CALC), showing all your working:

A.

B.

C.

D.

E.

F.

G.

• IB Questionbank Maths SL 25

34. If and write in terms of A and B:

A.

B.

C.