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IB Mathematics AA HL - Popular Quizzes

Exponents & Logs

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Question 1

no calculator

easy

[Maximum mark: 5]

Consider a=log6364×log6263×log6162××log23a = \log_{63}64\times\log_{62}63\times\log_{61}62\times\dots\times\log_{2}3. Given that aZa\in\mathbb{Z}, find the value of aa.

easy

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Question 2

no calculator

easy

[Maximum mark: 5]

Solve the equation log2(x22x+1)=1+log2(x1)\log_2(x^2-2x+1) = 1 + \log_2(x-1).

easy

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Question 3

no calculator

easy

[Maximum mark: 6]

  1. Write down the value of

    1. log381\log_3 81;

    2. log2(18)\log_2\Big(\dfrac{1}{8}\Big);

    3. log255\log_{25} 5. [3]

  2. Hence solve log381+log2(18)+log255=log9x\log_3 81 + \log_2\Big(\dfrac{1}{8}\Big) + \log_{25} 5 = \log_{9} x.[3]

easy

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Question 4

no calculator

easy

[Maximum mark: 5]

Find the values of xx when 25x22x=(1125)4x+225^{x^2-2x} = \left(\dfrac{1}{125}\right)^{4x+2}.

easy

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Question 5

no calculator

easy

[Maximum mark: 6]

Find the value of

  1. log798log72\log_7 98 - \log_7 2; [2]

  2. 49log7649^{\log_7 6}. [4]

easy

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Question 6

no calculator

easy

[Maximum mark: 5]

Solve the equation 9x+23x+1=19^x + 2\cdot3^{x+1} = 1.

easy

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Question 7

calculator

medium

[Maximum mark: 5]

Solve the equation 146x=64x+314^{6x} = 64^{x+3} for xx. Express your answer in terms of ln2\ln 2 and ln7\ln 7.

medium

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Question 8

no calculator

medium

[Maximum mark: 5]

Find the integer values of aa and bb for which

a+blog47+60log814=0.\begin{aligned} a + b\log_4 7 + 60\log_{8} 14 &= 0.\end{aligned}

medium

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Question 9

no calculator

hard

[Maximum mark: 8]

The first three terms of a geometric sequence are lnx9\ln x^9, lnx3\ln x^3, lnx\ln x, for x>0x > 0.

  1. Find the common ratio. [3]

  2. Solve k=133klnx=27\displaystyle \sum_{k=1}^\infty 3^{3-k}\ln x = 27. [5]

hard

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