1. Let f(x) = 3 ln x and g(x) = ln 5x 3 . (a) Express g(x) in the form f(x) + In a, where a E Z+. (b) The graph of g is a transformation of the graph of f. Give a full geometric description of this transformation. (4) (3) (Total 7 marks) 2. Let f(x) = log3 Vx , for x > 0. (a) Show that f 1(x) = 32x (2) (b) Write down the range of f-1. Let g(x) = log3 x, for x > 0. (c) Find the value of (f-1 · g)(2), giving your answer as an integer. (1) (Total 7 marks) (4) 3. Solve log2.x + log2(x - 2) = 3, for x > 2. (Total 7 marks) 4. Let A = 9e* e ex e 3x x 1. (a) Find an expression for det A. (2) IB Questionbank Maths SL 1
(b) Find the value of x for which A has no inverse. Express your answer in the form a ln b, where a, b E Z. (5) (Total 7 marks) 5. (a) Find log2 32. (1) (b) ) Given that log2 8 y 32x - can be written as px + qy, find the value of p and of q. (4) (Total 5 marks) 6. Let f(x) = k log2 x. (a) Given that f-1(1) = 8, find the value of k. (3) (b) Find f1(2). (4) (Total 7 marks) 7. Given that p = loga 5, q = loga 2, express the following in terms of p and/or q. (a) loga 10 (b) loga 8 IB Questionbank Maths SL 2
(c) loga 2.5 (Total 6 marks) 8. (a) Let logc 3 = p and log, 5 = q. Find an expression in terms of p and q for (i) log c 15; (ii) log c25. (b) Find the value of d if log a 6 = 1 2 . 9. Let ln a = p, ln b = q. Write the following expressions in terms of p and q. (Total 6 marks) (a) ln a 3b (b) In b (Total 6 marks) IB Questionbank Maths SL 3