ExpLog_NoGDC

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  IB Questionbank Maths SL 1 1.  Let  f  (  x ) = log 3  x , for   x > 0. (a) Show that  f   –  1 (  x ) = 3 2  x . (2) (b) Write down the range of   f   –  1 . (1) Let  g (  x ) = log 3    x , for   x > 0. (c) Find the value of (  f  –  1  °  g )(2), giving your answer as an integer. (4) (Total 7 marks) 2.  Solve log 2  x  + log 2 (  x    –   2) = 3, for   x > 2. (Total 7 marks) 3.  (a) Find log 2  32. (1) (b) Given that log 2         y x 832  can be written as  px  + qy , find the value of  p  and of q . (4) (Total 5 marks) 4.  Let  f  (  x ) =  k log 2    x . (a) Given that  f   –  1 (1) = 8, find the value of k  . (3)  IB Questionbank Maths SL 2 (b) Find   f   –  1      32 . (4) (Total 7 marks) 5.  Given that  p  = log a  5, q  = log a  2, express the following in terms of  p  and/or q . (a) log a  10 (b) log a  8 (c) log a  2.5 (Total 6 marks) 6.  (a) Let log c  3 =  p  and log c  5 = q . Find an expression in terms of  p  and q  for (i) log c  15; (ii) log c  25. (b) Find the value of d   if log d   6 = 21 . (Total 6 marks) 7.  Let ln a  =  p , ln b  = q . Write the following expressions in terms of  p  and q . (a) ln a 3 b  (b) ln      ba   (Total 6 marks)  IB Questionbank Maths SL 3 8.  Let  p  = log 10    x , q  = log 10    y  and r   = log 10    z . Write the expression log 10       z y x 2  in terms of  p , q  and r  .  Working:  Answer  : …………………………………………..   (Total 6 marks) x 9.  Let a  = log  x , b  = log  y , and c  = log  z . Write log      32  z y x  in terms of a , b  and c . Working:  Answer  : …………………………………………........   (Total 6 marks)  IB Questionbank Maths SL 4 10.  Given that log 5    x  =  y , express each of the following in terms of  y . (a) log 5  x 2  (b) log 5        x 1  (c) log 25  x Working:  Answers : (a) .................................................................. (b) .................................................................. (c) .................................................................. (Total 6 marks)
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