Maths Worksheet - Inverses, Exponentials And Logarithms

SAEP Matric Success – Zisukhanyo Maths Worksheet Tuesday 3rd March 2009 Inverses, Exponentials and Logarithms 1. Complete: a) log2 8 = d) log2 16 × log2 8 =

b) log7 7 = e) log 32 ÷ log 8 =

c) log3 27 + log3 3 =

2. Solve for x: a) log5 x = 2 d) log2 8 + log3 x = 4

b) –log5 x = 2 e) 2log x = 4-1

c) log x3 = 6

3. Simplify: a) 2a6 . 4a3 = d) -50 =

b) 2n . 23 = e) (-a)0 =

c) (4x2y)3 = f) (2n-1)2 =

4. Solve for x: a) 2 x = 64 d) 9x = 27x – 1

b) 13x = 1 e) -7x = -1

c) (0,2)x = 25 f) 2(x/5) = 1/32

5. Determine the value of a in the equation y = ax if its graph passes through the point: a) (1 ; 2) b) (2 ; 16) c) (-2 ; 16) d) (-1/3 ; 9) e) (1/2 ; 25) f) (0 ; 1) 6. Sketch the following pair of graphs on the same set of axes. (Use a different set of axes for each pair). In each case, state the line about which each pair of graphs is symmetrical a) y = 5x ; y = (1/5) x b) y = 4 x ; y = 4-x x x c) y = 3 ; y = -3 d) y = 2x ; x = 2y 7. a) Sketch the graph of y = f(x) = log2 x b) Explain why f is a function c) Give the domain and range of f d) State all intercepts of f with the axes e) On the same set of axes, sketch the graphs of y = log3 x and y = log4 x f) Are these functions one-to-one or many-to-one? Give a reason. g) Are there functions increasing or decreasing? Give a reason. 8. Determine the domain and range of: y = log2 (15 – 2x – x2) 9. Sketch f(x) = (1/2)x and its inverse f-1 on the same system of axes. a) Determine f-1(x) = … b) h is the mirror image of f about the x-axis. Determine h(x) c) k is the mirror image of f about the y-axis. Determine k(x)