Topical Revision Paper 5 Unit 5 Exponents & Logarithms Students

Topical Revision Paper 5 Term 2 Unit 5: Exponents & Logarithms Question 1: (i) Show that   2 333log 1 log 3 log 3( 1)xx    . [4] (ii) Hence, solve the equation    3 33log 1 log 1 log 3xx    . [4] Answer : (ii) 1 (n.a.) or 23xx Question 2: Solve the simultaneous equations yx xy 84 2 log2log 7log   [4] Answer : 8 , 16yx Question 3: Solve for x , given that 2 1 2 43 3 3 9 x x x   . [4] Answer : lg 2 or 0.631lg 3x or 2lg 3 or 0.369lg3x Question 4: Solve the following equations (a) 8 2 125log [2 log ( 4)] log 5x   (b) 2ln lg1.6ye  Answer : (a) 5x (b) 0.452y Question 5: The mass, m grams, of a radioactive substance after t years is given by the formula ktm ae  , where a and k are constants. At the beginning, the mass of radioactive substance is 83 g. After 35 years, there was only 26 g of the radioactive substance left. (i) Find the value of a and of k . [4] (ii) Sketch the graph of m against t. [2]

Answer : (i) 83a 26ln 83 0.033235k 