IB Mathematics AA HL  Popular Quizzes
Exponents & Logs
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Question 1
[Maximum mark: 5]
Consider $a = \log_{63}64\times\log_{62}63\times\log_{61}62\times\dots\times\log_{2}3$. Given that $a\in\mathbb{Z}$, find the value of $a$.
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Question 2
[Maximum mark: 5]
Solve the equation $\log_2(x^22x+1) = 1 + \log_2(x1)$.
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Question 3
[Maximum mark: 6]

Write down the value of

$\log_3 81$;

$\log_2\Big(\dfrac{1}{8}\Big)$;

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


Hence solve $\log_3 81 + \log_2\Big(\dfrac{1}{8}\Big) + \log_{25} 5 = \log_{9} x$.[3]
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Question 4
[Maximum mark: 5]
Find the values of $x$ when $25^{x^22x} = \left(\dfrac{1}{125}\right)^{4x+2}$.
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Question 5
[Maximum mark: 6]
Find the value of

$\log_7 98  \log_7 2$; [2]

$49^{\log_7 6}$. [4]
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Question 6
[Maximum mark: 5]
Solve the equation $9^x + 2\cdot3^{x+1} = 1$.
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Question 7
[Maximum mark: 5]
Solve the equation $14^{6x} = 64^{x+3}$ for $x$. Express your answer in terms of $\ln 2$ and $\ln 7$.
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Question 8
[Maximum mark: 5]
Find the integer values of $a$ and $b$ for which
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Question 9
[Maximum mark: 8]
The first three terms of a geometric sequence are $\ln x^9$, $\ln x^3$, $\ln x$, for $x > 0$.

Find the common ratio. [3]

Solve $\displaystyle \sum_{k=1}^\infty 3^{3k}\ln x = 27$. [5]
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