Math SL Test: Exponents & Logarithms - High School

MATH SL TEST EXPONENTS - LOGARITHMS by Christos Nikolaidis Marks:____/50 Name:____________________________________ Date: Grade: ______ 12-1-2016 Questions 1. [Maximum mark: 6] Solve the following equations (a) (b) 2 5 x = 25 x 1 = 8 4x [3 marks] [3 marks] ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... Page 1 2. [Maximum mark: 6] Solve the following equations (a) e x +1 = 9 [2 marks] (b) ln( x + 1) = 2 [2 marks] (c) e 2 ln x = 9 [2 marks] ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... Page 2 3. [Maximum mark: 6] Let ln x = p and ln y = q . Express the following in terms of p and q. (a) ln x 2 y (b) ln (c) log y x [2 marks] x [2 marks] y [2 marks] ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... Page 3 4. [Maximum mark: 6] Solve the equation log 3 ( x − 4) = 1 + log 9 x [6 marks] ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... Page 4 5. [Maximum mark: 6] Solve the exponential equation 3 x −1 = 2 x +3 . ln a Give your answer in the form x = , where a, b are rational numbers. ln b ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... Page 5 6. [Maximum mark: 10] Solve the equations (a) e 2 x − 14 = 5e x [5 marks] [5 marks] 2 (b) (ln x ) − 14 = 5 ln x ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... Page 6 7. [Maximum mark: 10] Consider the function f ( x) = 3e x − 4 (a) Find the domain and the range of f. −1 [2 marks] (b) Find f ( x) (c) Sketch the graphs of f and f −1 by indicating clearly any asymptotes and the exact values of the intersections with the axes. ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... Page 7 [3 marks] [5 marks] EXTRA SPACE (if needed) ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... 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Math SL Test: Exponents & Logarithms - High School

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