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CAT 2025 Lesson : Logarithm - Past Questions

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Question 1

If f(x) = log(1+x1−x)\mathrm{log} \left( \dfrac{1 + x}{1 - x} \right), then f(x) + f(y) = ?
[CAT 2002]

f(x + y)
f(1 + xy)
(x + y) f(1 + xy)
f(x+y1+xy)\left( \dfrac{x + y}{1 + xy} \right)

Question 2

If log10x−log10x3=6logx10\mathrm{log}_{10}{x} - {log}_{10}{\sqrt[3]{x} = 6 \mathrm{log}_{x}{10}}, then the value of x is
[IIFT 2013]

10
30
100
1000

Question 3

The value of the expression ∑i=21001logi100!\sum\limits_{i = 2}^{100}{\dfrac{1}{\mathrm{log}_{i}{100!}}} is
[XAT 2014]

0.01
0.1
1
10
100
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