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Logarithms - Past Year Questions

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Q1:

Let a=(log⁡74)(log⁡75−log⁡72)log⁡725(log⁡78−log⁡74)a = \dfrac{(\log_7 4)(\log_7 5 - \log_7 2)}{\log_{7} 25 (\log_7 8 - \log_7 4)}. Then the value of 5a5^a is
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Option: 2
Correct Answer
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Q2:

The numbers 220242^{2024} and 520245^{2024} are expanded and their digits are written out consecutively on one page. The total number of digits written on the page is
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Option: 2
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Q3:

If log⁡4x=a\log_4 x = a and log⁡25x=b\log_{25} x = b, then log⁡x10\log_x 10 is
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Option: 3
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Q4:

If 4log⁡2x−4x+9log⁡3y−16y+68=04^{\log_2{x}} - 4x + 9^{\log_3{y}} - 16y + 68 = 0, then y−xy - x equals:
6
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Q5:

If log⁡(cosx)(sinx)+log⁡(sinx)(cosx)=2,\log_{(cos x)}(sin x) + \log_{(sin x)}(cos x) = 2, then the value of xx is
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Option: 2
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Q6:

Let a,b,ca, b, c be real numbers greater than 1, and nn be a positive real number not equal to 1. If logn(log2a)=1;logn(log2b)=2log_n(log_2a) = 1; log_n(log_2b) = 2 and logn(log2c)=3log_n(log_2c) = 3 then which of the following is true?
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Option: 4
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Q7:

The product of the roots of the equation log⁡22(log⁡2x)2−5log⁡2x+6=0\log_{2} 2^{(\log_{2}x)^{2}} -5 \log_{2}x+6=0 is
32
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Q8:

The set of real values of xx for which the inequality log⁡278≤log⁡3x<91log⁡23\log _{27} 8 \leq \log _{3} x \lt 9^{\frac{1}{\log _{2} 3}} holds is
Answer options
Option: 1
Correct Answer
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Q9:

If log⁡(x2)y+log⁡(y2)x=1\log _{\left(x^{2}\right)} y+\log _{\left(y^{2}\right)} x=1 and y=x2−30y=x^{2}-30, then the value of x2+y2x^{2}+y^{2} is ___________.
72
Correct Answer
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Q10:

Suppose that log⁡2[log⁡3(log⁡4a)]=log⁡3[log⁡4(log⁡2b)]=log⁡4[log⁡2(log⁡3c)]=0\log_2[\log_3 (\log_4a)] = \log_3 [\log_4 (\log_2b)] = \log_4 [\log_2 (\log_3c)] = 0 then the value of a+b+ca + b + c is
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Option: 3
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Q11:

If log⁡5(log⁡8(x2−1))=0\log_5(\log_8(x^2 - 1)) = 0, then a possible value of xx is
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Option: 4
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Q12:

The value of (0.04log5(14+18+116+...))(0.04^{log_{\sqrt{5}}(\frac{1}{4} + \frac{1}{8} + \frac{1}{16} + ...)}) is __________.
16
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Explanation →

Q13:

The value of (log⁡330)−1+(log⁡4900)−1+(log⁡530)−1(\log_{3} 30)^{-1} + (\log_{4} 900)^{-1} + (\log_{5} 30)^{-1} is
Answer options
Option: 4
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Q14:

The inequality log⁡23x−12−x<1\log_{2} \frac{3x - 1}{2 - x} < 1 holds true for
Answer options
Option: 1
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Q15:

The inequality log⁡af(x)<log⁡ag(x)\log_{a}{f(x)} < \log_{a}{g(x)} implies that
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Option: 1
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Q16:

Suppose that a, b, and c are real numbers greater than 1. Then the value of 11+log⁡a2bca+11+log⁡b2cab+11+log⁡c2abc\dfrac{1}{1+\log_{a^2 b} \frac{c}{a}} + \dfrac{1}{1+\log_{b^2 c} \frac{a}{b}} + \dfrac{1}{1+\log_{c^2 a} \frac{b}{c}} is
3
Correct Answer
Explanation →

Q17:

If x,y,zx, y, z are positive real numbers such that x12=y16=z24x^{12} = y^{16} = z^{24} and the three quantities 3log⁡yx,4log⁡zy,nlog⁡xz3 \log_y x, 4 \log_z y, n \log_x z are in arithmetic progression, then the value of nn is
16
Correct Answer
Explanation →

Logarithms - Past Year Questions (Free PDF Download)

Practice with our comprehensive collection of Logarithms Past Year Questions (PYQs of IPMAT Indore, IPMAT Rohtak & JIPMAT) with detailed solutions. These questions are carefully curated from previous year papers to help you understand the exam pattern and improve your preparation.

Our free resources include handwritten solutions for all questions, making it easier to understand the concepts and approach. Use these PYQs to assess your preparation level and identify areas that need more focus. No login required. Compilation of IPMAT Indore, IPMAT Rohtak & JIPMAT Questions!