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Mathematics Logarithm Advance Logarithm Questions Q. #576 (CAT-I)

যদি log₅ (x² + x) - log₅ (x + 1) = 2 হয়, তবে x এর মান কত?

A. 5

B. 10

C. 25

D. 30

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Correct Answer: Option C

Option C is the correct answer according to official curriculum guidelines.

Mathematics Logarithm Advance Logarithm Questions Q. #575 (CAT-I)

যদি a = log₂₄ 12, b = log₃₆ 24 এবং c = log₄₈ 36 হয়, তবে 1 + abc এর মান কত?

A. abc

B. 2bc

C. 2ab

D. 2ac

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Correct Answer: Option B

Option B is the correct answer according to official curriculum guidelines.

Mathematics Logarithm Advance Logarithm Questions Q. #574 (CAT-I)

1/(1+logₐ bc) + 1/(1+log_b ca) + 1/(1+log_c ab) এর মান কত?

A. 1

B. 0

C. abc

D. log(abc)

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Correct Answer: Option A

Option A is the correct answer according to official curriculum guidelines.

Mathematics Logarithm Advance Logarithm Questions Q. #573 (CAT-I)

2 log₁₀ 5 + log₁₀ 8 - 1/2 log₁₀ 4 এর মান কত?

A. 0

B. 1

C. 3

D. 2

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Correct Answer: Option D

Option D is the correct answer according to official curriculum guidelines.

Mathematics Logarithm Advance Logarithm Questions Q. #572 (CAT-I)

logₓ 2 + logₓ 4 + logₓ 8 = 6 সমীকরণে x এর মান কত?

A. √2

B. 4

C. 2

D. 8

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Correct Answer: Option C

Option C is the correct answer according to official curriculum guidelines.

Mathematics Logarithm Advance Logarithm Questions Q. #571 (CAT-I)

যদি log₃ 2, log₃(2ˣ - 5) এবং log₃(2ˣ - 7/2) সমান্তর প্রগতিতে (AP) থাকে, তবে x এর মান কত?

A. 2

B. 3

C. 4

D. 5

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Correct Answer: Option B

Option B is the correct answer according to official curriculum guidelines.

Mathematics Logarithm Advance Logarithm Questions Q. #570 (CAT-I)

যদি a² + b² = 7ab হয়, তবে log[(a+b)/3] এর মান কোনটি?

A. 1/2(log a + log b)

B. log a + log b

C. 1/2(log a - log b)

D. 2(log a + log b)

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Correct Answer: Option A

Option A is the correct answer according to official curriculum guidelines.

Mathematics Logarithm Advance Logarithm Questions Q. #569 (CAT-I)

log₁₀ (x-15) + log₁₀ 10 = 4 হলে x এর মান কত?

A. 115

B. 985

C. 1000

D. 1015

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Correct Answer: Option D

Option D is the correct answer according to official curriculum guidelines.

Mathematics Logarithm Advance Logarithm Questions Q. #568 (CAT-I)

যদি (log x) / (b-c) = (log y) / (c-a) = (log z) / (a-b) হয়, তবে xᵃ yᵇ zᶜ এর মান কত?

A. 0

B. -1

C. 1

D. xyz

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Correct Answer: Option C

Option C is the correct answer according to official curriculum guidelines.

Mathematics Logarithm Advance Logarithm Questions Q. #567 (CAT-I)

log₂ 10 - log₈ 125 এর সরলতম মান কত?

A. 0

B. 1

C. log₂ 5

D. 2

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Correct Answer: Option B

Option B is the correct answer according to official curriculum guidelines.

Mathematics Logarithm Advance Logarithm Questions Q. #566 (CAT-I)

যদি logₓ (4x-3) = 2 হয়, তবে x এর সঠিক মান কোনটি?

A. 3

B. 1

C. 1 অথবা 3

D. কোনোটিই নয়

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Correct Answer: Option A

Option A is the correct answer according to official curriculum guidelines.

Mathematics Logarithm Advance Logarithm Questions Q. #565 (CAT-I)

7^{log₇(x²-4x+5)} = x-1 সমীকরণটির সমাধান কোনটি?

A. x = 1

B. x = 3

C. x = 1, 2

D. x = 2

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Correct Answer: Option D

Option D is the correct answer according to official curriculum guidelines.

Mathematics Logarithm Advance Logarithm Questions Q. #564 (CAT-I)

যদি logₖ x ⋅ log₅ k = 3 হয়, তবে x এর মান কত হবে?

A. 15

B. 25

C. 125

D. 625

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Correct Answer: Option C

Option C is the correct answer according to official curriculum guidelines.

Mathematics Logarithm Advance Logarithm Questions Q. #563 (CAT-I)

যদি log₁₀ 2 = 0.3010 হয়, তবে 5²⁰ সংখ্যাটিতে কতগুলি অংক (digits) আছে?

A. 13

B. 14

C. 15

D. 20

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Correct Answer: Option B

Option B is the correct answer according to official curriculum guidelines.

Mathematics Logarithm Advance Logarithm Questions Q. #562 (CAT-I)

যদি log₂[log₃(log₂ x)] = 1 হয়, তবে x এর মান কত?

A. 512

B. 256

C. 128

D. 64

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Correct Answer: Option A

Option A is the correct answer according to official curriculum guidelines.