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Algebra - Logarithms - Previous Year IPM/BBA Questions

The best way to prepare for Algebra - Logarithms is by going through the previous year Algebra - Logarithms questions for IPMAT - Indore. Here we bring you all previous year Algebra - Logarithms IPMAT - Indore questions along with detailed solutions.

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It would be best if you clear your concepts before you practice previous year Algebra - Logarithms questions for IPMAT - Indore.

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1. IPMAT (I) 2023 QASA | Algebra - Logarithms IPMAT - Indore Question

The product of the roots of the equation $\log_{2} 2^{{(\log_{2} x)}^{2}}$ - 5log₂x + 6 = 0

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2. IPMAT (I) 2023 QA MCQ | Algebra - Logarithms IPMAT - Indore Question

Let a, b, c be real numbers greater than 1. and n be a positive real number not equal to I. If log_n(log₂ a) = 1, log_n(log₂b) = 2 and log_n(log₂c) = 3. then which of the following is true?

(a)
(aⁿ + b)ⁿ = ac
(b)
aⁿ + bⁿ = cⁿ
(c)
a + b = c
(d)
(b - a)ⁿ = (c - b)

3. IPMAT (I) 2023 QA MCQ | Algebra - Logarithms IPMAT - Indore Question

If log_cosxsinx + log_sinxcosx = 2, then the value of x is

(a)
nπ/4 + π/4, n is an integer
(b)
2nπ + π/4, n is an integer
(c)
nπ + π/4, n is an integer
(d)
nπ/4, n is an integer

4. IPMAT (I) 2022 QASA | Algebra - Logarithms IPMAT - Indore Question

$\log_{x^{2}} (y)$ + $\log_{y^{2}} (x)$ = 1 and y = x² - 30, then the value of x² + y² is:

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Answer: 72

Text Explanation :

Given, $\log_{x^{2}} (y)$ + $\log_{y^{2}} (x)$ = 1

⇒ $\frac{\log_{x} (y)}{2}$ + $\frac{\log_{y} (x)}{2}$ = 1

⇒ log_xy + log_yx = 2

Now, log_xy and log_yx are reciprocal of each other and their sum is 2. Sum of a number and its reciprocal is always greater than or equal to 2. Equality is true when the number and reciprocal are both equal to 1.

∴ log_xy = 1
⇒ x = y

Now, y = x² - 30 [y = x]
⇒ x² - x - 30 = 0
⇒ (x - 6)(x + 5) = 0
⇒ x = 6 [x = -5 is rejected as log is not defined for negative numbers.]
∴ y = 6

∴ x² + y² = 6² + 6² = 72

Hence, 72.

5. IPMAT (I) 2022 QA MCQ | Algebra - Logarithms IPMAT - Indore Question

The set of real values of x for which the inequality $\log_{27} (8)$ ≤ $\log_{3} (x)$ < $9^{\frac{1}{\log_{2} (3)}}$ holds is

(a)
[2, 81)
(b)
(2, 27)
(c)
[2, 81]
(d)
(2, 27]

Answer: Option A

Text Explanation :

Given, $\log_{27} (8)$ ≤ $\log_{3} (x)$ < $9^{\frac{1}{\log_{2} (3)}}$

⇒ $\log_{3^{3}} (2^{3})$ ≤ $\log_{3} (x)$ < $9^{\log_{3} (2)}$

⇒ $\frac{3}{3} \log_{3} (2)$ ≤ $\log_{3} (x)$ < $2^{\log_{3} (9)}$

⇒ $\log_{3} (2)$ ≤ $\log_{3} (x)$ < $2^{2}$

⇒ $\log_{3} (2)$ ≤ $\log_{3} (x)$ < 4

⇒ $\log_{3} (2)$ ≤ $\log_{3} (x)$ < $\log_{3} (3^{4})$

⇒ 2 ≤ x < 81

∴ x ∈ [2, 81)

Hence, option (a).

6. IPMAT (I) 2021 QA MCQ | Algebra - Logarithms IPMAT - Indore Question

Suppose that log₂[log₃(log₄a)] = log₃[log₄(log₂b)] = log₄[log₂(log₃c)] = 0 then the value of a + b + c is

(a)
105
(b)
71
(c)
89
(d)
37

7. IPMAT (I) 2020 QASA | Algebra - Logarithms IPMAT - Indore Question

The value of $0 . 04^{\log_{\sqrt{5}} (\frac{1}{4} + \frac{1}{8} + \frac{1}{16} + . . .)}$ is _________.

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Answer: 16

Text Explanation :

Given, $0 . 04^{\log_{\sqrt{5}} (\frac{1}{4} + \frac{1}{8} + \frac{1}{16} + . . .)}$

= $0 . 04^{\log_{\sqrt{5}} (\frac{1 / 4}{1 - 1 / 2})}$

= $0 . 04^{\log_{\sqrt{5}} (\frac{1}{2})}$

= ${(5^{- 2})}^{\log_{\sqrt{5}} (\frac{1}{2})}$

= ${(5^{- 2})}^{\log_{5^{1 / 2}} (\frac{1}{2})}$

= ${(5^{- 2})}^{2 \log_{5} (\frac{1}{2})}$

= $5^{- 4 \log_{5} (\frac{1}{2})}$

= $5^{\log_{5} {(\frac{1}{2})}^{- 4}}$

= $5^{\log_{5} 16}$

= $16^{\log_{5} 5}$

= 16.

Hence, 16.

8. IPMAT (I) 2020 QA MCQ | Algebra - Logarithms IPMAT - Indore Question

If log₅log₈(x² - 1) = 0, then a possible value of x is

(a)
2√2
(b)
√2
(c)
2
(d)
3

9. IPMAT (I) 2020 QA MCQ | Algebra - Logarithms IPMAT - Indore Question

Given f(x) = x² + log₃x and g(y) = 2y + f(y), then the value of g(3) equals

(a)
16
(b)
15
(c)
25
(d)
26

10. IPMAT (I) 2019 QASA | Algebra - Logarithms IPMAT - Indore Question

Suppose that a, b, and c are real numbers greater than 1. Then the value of $\frac{1}{1 + \log_{a^{2} b} (\frac{c}{a})}$ + $\frac{1}{1 + \log_{b^{2} c} (\frac{a}{b})}$ + $\frac{1}{1 + \log_{c^{2} a} (\frac{b}{c})}$ is

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11. IPMAT (I) 2019 QASA | Algebra - Logarithms IPMAT - Indore Question

If x, y, z are positive real numbers such that x¹² = y¹⁶ = z²⁴,and the three quantities 3log_yx, 4log_zy, nlog_xz are in arithmetic progression, then the value of n is

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12. IPMAT (I) 2019 QA MCQ | Algebra - Logarithms IPMAT - Indore Question

The inequality $\log_{2} (\frac{3 x - 1}{2 - x})$ < 1 holds true for

(a)
x ∈ (1/3, 1)
(b)
x ∈ (1/3, 2)
(c)
x ∈ (0, 1/3) ∪ (1, 2)
(d)
x ∈ (-∞, 1)

13. IPMAT (I) 2019 QA MCQ | Algebra - Logarithms IPMAT - Indore Question

The value of log₃30⁻¹+ log₄900⁻¹+ log₅30⁻¹ is

(a)
0.5
(b)
30
(c)
2
(d)
1

Algebra - Logarithms - Previous Year IPM/BBA Questions

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