Exponents and Logarithms
description
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.
Write log in terms of a, b and c.
(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.