1. Solve log2x + log2(x – 2) = 3, for x > 2.
(Total 7 marks)
2. (a) Find log2 32.
(1)
32 x
(b) Given that log2 y can be written as px + qy, find the value of p and of q.
8
(4)
(Total 5 marks)
3. 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)
4. (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.
1
(b) Find the value of d if log d 6 = .
2
(Total 6 marks)
5. Let ln a = p, ln b = q. Write the following expressions in terms of p and q.
(a) ln a3b
a
(b) ln
b
(Total 6 marks)
6. Find the exact solution of the equation 92x = 27(1–x).
Working:
Answer:
....……………………………………..........
(Total 6 marks)
7. (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.
Working:
Answers:
(a) ..................................................................
(b) ..................................................................
(Total 6 marks)
8. Solve the equation log27 x = 1 – log27 (x – 0.4).
Working:
Answer:
......................................................................
(Total 6 marks)
9. Given that log5 x = y, express each of the following in terms of y.
(a) log5 x2
(b) log5 1
x
(c) log25 x
Working:
Answers:
(a) ..................................................................
(b) ..................................................................
(c) ..................................................................
(Total 6 marks)
1
10. Solve the equation log9 81 + log9 + log9 3 = log9 x.
9
Working:
Answer:
.......................................................................
(Total 4 marks)
11. If loga 2 = x and loga 5 = y, find in terms of x and y, expressions for
(a) log2 5;
(b) loga 20.
Working:
Answers:
(a) ..................................................................
(b) ..................................................................
(Total 4 marks)
2x
12. Solve the equation 9x–1 = 1 .
3
Working:
Answer:
......................................................................
(Total 4 marks)
13. Solve the equation log3(x + 17) – 2 = log3 2x.
(Total 5 marks)
14. Solve the equation 22x+2 – 10 × 2x + 4 = 0, x ∈ .
(Total 6 marks)
