Exponents and Logarithms

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Transcript of Exponents and Logarithms

  • IB Questionbank Maths SL 1

    Exponents And Logarithms

    1. Solve the following equations.

    (a) logx 49 = 2

    (3)

    (b) log2 8 = x

    (2)

    (c) log25 x =

    (3)

    (d) log2 x + log2(x 7) = 3

    (5)

    (Total 13 marks)

    2. Solve the equation log9 81 + log9 + log9 3 = log9 x.

    (Total 4 marks)

    3. Solve the equation 43x1

    = 1.5625 102.

    (Total 4 marks)

    2

    1

    9

    1

  • IB Questionbank Maths SL 2

    4. Solve the equation 9x1

    =

    (Total 4 marks)

    5. Let log10P = x , log10Q = y and log10R = z. Express in terms of x , y and z.

    (Total 4 marks)

    6. If loga 2 = x and loga 5 = y, find in terms of x and y, expressions for

    (a) log2 5;

    .31

    2x

    2

    310log

    QR

    P

  • IB Questionbank Maths SL 3

    (b) loga 20.

    (Total 4 marks)

    7. Let ln a = p, ln b = q. Write the following expressions in terms of p and q.

    (a) ln a3b

    (b) ln

    (Total 6 marks)

    8. Solve the equation log27 x = 1 log27 (x 0.4).

    (Total 6 marks)

    b

    a

  • IB Questionbank Maths SL 4

    9. (a) Given that log3 x log3 (x 5) = log3 A, express A in terms of x.

    (b) Hence or otherwise, solve the equation log3 x log3 (x 5) = 1.

    (Total 6 marks)

    10. Given that log5 x = y, express each of the following in terms of y.

    (a) log5 x2

    (b) log5

    (c) log25 x

    x

    1

  • IB Questionbank Maths SL 5

    (Total 6 marks)

    11. Let a = log x, b = log y, and c = log z.

    Write log in terms of a, b and c.

    (Total 6 marks)

    12. Let p = log10 x, q = log10 y and r = log10 z.

    Write the expression log10 in terms of p, q and r.

    (Total 6 marks)

    13. Find the exact solution of the equation 92x

    = 27(1x)

    .

    (Total 6 marks)

    14. Solve log2x + log2(x 2) = 3, for x > 2.

    3

    2

    z

    yx

    zy

    x2

  • IB Questionbank Maths SL 6

    (Total 7 marks)

    15. (a) Find log2 32.

    (1)

    (b) Given that log2 can be written as px + qy, find the value of p and of q.

    (4)

    (Total 5 marks)

    16. (a) Let logc 3 = p and logc 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 = .

    (Total 6 marks)

    y

    x

    8

    32

    2

    1

  • IB Questionbank Maths SL 7

    17. Given that p = loga 5, q = loga 2, express the following in terms of p and/or q.

    (a) loga 10

    (b) loga 8

    (c) loga 2.5

    (Total 6 marks)

    18. (a) Given that (2x)2 + (2

    x) 12 can be written as (2x + a)(2x + b), where a, b , find the value of a and of b.

    (b) Hence find the exact solution of the equation (2x)2 + (2

    x) 12 = 0, and explain why there is only one solution.

    (Total 6 marks)

  • IB Questionbank Maths SL 8

    EXTRA PRACTISE

    19. Solve the following logarithmic equations

  • IB Questionbank Maths SL 9

    20. Solve the following logarithmic equations:

  • IB Questionbank Maths SL 10

    21. Solve the following logarithmic equations:

  • IB Questionbank Maths SL 11

  • IB Questionbank Maths SL 12

    22. Solve the following equations, giving exact answers:

  • IB Questionbank Maths SL 13

    23. Solve the following equations, giving exact answers:

  • IB Questionbank Maths SL 14

    24. Solve the following simultaneous equations:

    25. Solve the following equations:

  • IB Questionbank Maths SL 15

  • IB Questionbank Maths SL 16

    26. Solve the following equations:

    27. Solve the following equations (Hidden Quadratic Equations):

  • IB Questionbank Maths SL 17

    28.

  • IB Questionbank Maths SL 18

    29.

    30.

  • IB Questionbank Maths SL 19

  • IB Questionbank Maths SL 20

    31. Solve the following equations:

    A.

    B.

  • IB Questionbank Maths SL 21

    C.

    D.

  • IB Questionbank Maths SL 22

    E.

    F.

  • IB Questionbank Maths SL 23

    32. Write down the following equations without logarithms:

    A.

    B.

    C.

    D.

    E.

    F.

    G.

    H.

  • IB Questionbank Maths SL 24

    33. Evaluate the following (without CALC), showing all your working:

    A.

    B.

    C.

    D.

    E.

    F.

    G.

  • IB Questionbank Maths SL 25

    34. If and write in terms of A and B:

    A.

    B.

    C.