How to prepare for Quantitative Aptitude for the CAT>Chapter 23 - Logarithms>Level of Difficulty>Q 24

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IMPORTANT

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If $\log_{10} 242 = a, \log_{10} 80 = b$ and $\log_{10} 45 = c$ , express $\log_{10} 66$ in terms of a, b and c.

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Important Questions on Logarithms

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CAT

IMPORTANT

How to prepare for Quantitative Aptitude for the CAT>Chapter 23 - Logarithms>Level of Difficulty>Q 25

\log_{2} (9 - 2^{x}) = 10^{\log (3 - x)}

, solve for

x

.

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CAT

IMPORTANT

How to prepare for Quantitative Aptitude for the CAT>Chapter 23 - Logarithms>Level of Difficulty>Q 26

If

\frac{\log_{x}}{b - c} = \frac{\log_{y}}{c - a} = \frac{\log_{z}}{a - b}

. Mark all the correct options.

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CAT

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How to prepare for Quantitative Aptitude for the CAT>Chapter 23 - Logarithms>Level of Difficulty>Q 27

What will be the value of x if it is given that:

$\log_{x} {[\frac{1}{5} + \frac{1}{12} + \frac{1}{21} + \frac{1}{32} + \frac{1}{45} + . . . + \infty terms]}^{2} = 2 .$

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CAT

IMPORTANT

How to prepare for Quantitative Aptitude for the CAT>Chapter 23 - Logarithms>Level of Difficulty>Q 28

(\log_{4} x^{2}) ({xlog}_{27} 8) (\log_{x} 243)

is equal to?

EASY

CAT

IMPORTANT

How to prepare for Quantitative Aptitude for the CAT>Chapter 23 - Logarithms>Level of Difficulty>Q 29

For how many real values of x will the equation

\log_{3} \log_{6} (x^{3} - 18 x^{2} + 108 x) = \log_{2} \log_{4} 16

be satisfied?

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CAT

IMPORTANT

How to prepare for Quantitative Aptitude for the CAT>Chapter 23 - Logarithms>Level of Difficulty>Q 30

If

n = 12 \sqrt{3}

, then

\frac{1}{\log_{2} n} + \frac{1}{\log_{3} n} + \frac{1}{\log_{4} n} + \frac{1}{\log_{6} n} + \frac{1}{\log_{8} n} + \frac{1}{\log_{9} n} + \frac{1}{\log_{18} n} = ?

EASY

CAT

IMPORTANT

How to prepare for Quantitative Aptitude for the CAT>Chapter 23 - Logarithms>Level of Difficulty>Q 31

{(\log_{2} x)}^{2} + 2 \log_{2} x - 8 = 0

, Where x is a natural number. If

x^{p} = 64

, then what is the value of

x + p

?

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CAT

IMPORTANT

How to prepare for Quantitative Aptitude for the CAT>Chapter 23 - Logarithms>Level of Difficulty>Q 34

If 'p' and 'q' are integers and

\log_{p} (- q^{2} + 6 q - 8) + \log_{q} (- 2 p^{2} + 20 p - 48) = 0

. Then

p \times q = ?