Algebra - Logarithms - Previous Year CAT/MBA Questions

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

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1. XAT 2024 QADI | Algebra - Logarithms XAT Question

Consider the equation , where x is a real number log₅(x - 2) = 2log₂₅(2x - 4).

For how many different values of x does the given equation hold?

(a)
0
(b)
1
(c)
2
(d)
4
(e)
Infinitely many

2. XAT 2021 QADI | Algebra - Logarithms XAT Question

If log₄ m + log₄ n = log₂ (m + n) where m and n are positive real numbers, then which of the following must be true?

(a)
$\frac{1}{m}$ + $\frac{1}{n}$ = 1
(b)
m = n
(c)
m² + n² = 1
(d)
$\frac{1}{m}$ + $\frac{1}{n}$ = 2
(e)
No values of m and n can satisfy the given equation

Answer: Option E

Text Explanation :

log₄ mn = log₂ (m + n)

$\sqrt{m n}$ = (m + n)

Squaring on both sides

m² + n² + mn = 0

Since m, n are positive real numbers, no value of m and n satisfy the above equations.

3. XAT 2019 QADI | Algebra - Logarithms XAT Question

$\frac{\log (97 - 56 \sqrt{3})}{\log (\sqrt{7 + 4 \sqrt{3}})}$ equals which of the following?

(a)
-5
(b)
-3
(c)
None of the others
(d)
-4
(e)
-2

Answer: Option D

Video Explanation

Text Explanation :

Given $\frac{\log (97 - 56 \sqrt{3})}{\log (\sqrt{7 + 4 \sqrt{3}})}$

= $\frac{\log {(7 - 4 \sqrt{3})}^{2}}{\log {(7 + 4 \sqrt{3})}^{1 / 2}}$

Now, $7 + 4 \sqrt{3}$ = $\frac{1}{7 - 4 \sqrt{3}}$

⇒ $\frac{\log {(7 - 4 \sqrt{3})}^{2}}{\log {(7 + 4 \sqrt{3})}^{1 / 2}}$ = $\frac{\log {(7 - 4 \sqrt{3})}^{2}}{\log {(7 - 4 \sqrt{3})}^{- 1 / 2}}$ = $\frac{2}{- 1 / 2}$ = -4

Algebra - Logarithms - Previous Year CAT/MBA Questions

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