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406 . $\frac{\log \sqrt{27} + \log 8 - \log \sqrt{1000}}{\log 1.2}$

A. 1.052
B. 1.5
C. 3.5
D. 20.5

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Answer: Option B

Explanation:

\frac{\log \sqrt{27} + \log 8 - \log \sqrt{1000}}{\log 1.2} = \frac{\log \sqrt{3^{3}} + \log 2^{3} - \log \sqrt{{(2 \times 5)}^{3}}}{\log \frac{12}{10}} = \frac{\log 3^{\frac{3}{2}} + \log 2^{3} - \log (2^{\frac{3}{2}} \times 5^{\frac{3}{2}})}{\log \frac{6}{5}} = \frac{\log 3^{\frac{3}{2}} + \log 2^{3} - \log (2^{\frac{3}{2}} \times 5^{\frac{3}{2}})}{\log 6 - \log 5} = \frac{\frac{3}{2} \log 3 + 3 \log 2 - \frac{3}{2} \log 2 - \frac{3}{2} \log 5}{\log (3 \times 2) - \log 5} = \frac{\frac{3}{2} \log 3 + 3 \log 2 - \frac{3}{2} \log 2 - \frac{3}{2} \log 5}{\log 3 + \log 2 - \log 5} = \frac{\frac{3}{2} \log 3 + \frac{3}{2} \log 2 - \frac{3}{2} \log 5}{\log 3 + \log 2 - \log 5} = \frac{\frac{3}{2} (\log 3 + \log 2 - \log 5)}{\log 3 + \log 2 - \log 5} = \frac{3}{2} = 1.5

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407 . কোন শর্তে $a^{0} = 1 ?$

A. $a = 0$
B. $a ≢ 0$
C. $a > 0$
D. $a ≢ 1$

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Answer: Option B

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408 . $5^{x} + 8 . 5^{x} + 16 . 5^{x} = 1$ হলে x এর মান কত?

A. -1
B. 3
C. -2
D. $- \frac{1}{2}$

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Answer: Option C

Explanation:

দেওয়া আছে, 5^{x} {+8×5}^{x} {+16×5}^{x} =1 \Rightarrow 5^{x} (1 + 8 + 16) = 1 \Rightarrow 5^{x} \times 25 = 1 \Rightarrow 5^{x} = \frac{1}{25} \Rightarrow 5^{x} = (\frac{1}{5^{2}}) \Rightarrow 5^{x} = 5^{- 2} ∴ x = - 2

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409 . $\log_{5} (3 \sqrt{5}) (\sqrt{5})$ এর মান কোনটি?

A. $\frac{6}{5}$
B. $\sqrt{\frac{5}{6}}$
C. $\frac{5}{6}$
D. $\frac{1}{2}$

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Answer: Option C

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410 . সরল করুনঃ $3 \log \frac{36}{25} + \log {(\frac{2}{9})}^{3} - 2 \log \frac{16}{125}$

A. $\log^{2}$
B. $\log^{3}$
C. $\log^{5}$
D. $\log^{7}$

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Answer: Option A

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411 . ${\log_{3}}^{81}$ এর মান কত?

A. 4
B. 9
C. 3
D. 27

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Answer: Option A

Explanation:

{\log_{3}}^{81} = \log_{3} {(3)}^{4} = 4 {\log_{3}}^{3} = 4 \times 1 = 4

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বাংলাদেশ ডাক বিভাগ (মেট্রোপলিটন সার্কেল) পরিদর্শক-১৩.০৫.২০১৬

412 . $\log_{2} 64 + \log_{2} 8$ এর মান কত?

A. 9
B. 7
C. 28
D. 72

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Answer: Option A

Explanation:

{\log_{2}}^{64} + {\log_{2}}^{8} = {\log_{2}}^{2^{6}} + {\log_{2}}^{2^{3}} = 6 \times 1 + 3 \times 1 = 6 + 3 = 9

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১২ তম বেসরকারি প্রভাষক নিবন্ধন পরীক্ষা (12-06-2015)

413 . $\log_{x} = 144 = 4$ হলে , x এর মান কত?

A. $2 \sqrt{3}$
B. 3
C. 4
D. 12

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Answer: Option A

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414 . $\log_{5} x = 3$ হলে x = কত?

A. 120
B. 125
C. 225
D. 375

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Answer: Option B

Explanation:

\log 5 x = 3 \Rightarrow x = 5^{3} \Rightarrow x = 125

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415 . $\log 2 {\sqrt{5}}^{400 = x}$ হলে, x এর মান কত?

A. 4
B. 5
C. 8
D. 20

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Answer: Option A

Explanation:

\log_{2} {\sqrt{5}}^{400} = x \Rightarrow {(2 \sqrt{5})}^{x} = 400 \Rightarrow {(2 \sqrt{5})}^{x} = {(2 \sqrt{5})}^{4} ∴ x = 4

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416 . 5x0= কত?

B. 5x
C. 5
D. 1

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Answer: Option D

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417 . ${(\sqrt{3})}^{6} =$ কত?

A. 9
B. 27
C. 18
D. 81

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Answer: Option B

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প্রবাসী কল্যাণ ও বৈদেশিক কর্মসংস্থান মন্ত্রণালয়ের সহকারী পরিচালক-১১.০৫.২০১২

418 . $\log_{3} (\frac{1}{9}) = ?$

A. 2
B. 3
C. -2
D. -3

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Answer: Option C

Explanation:

\log_{3} (\frac{1}{2})

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পরিসংখ্যান ও তথ্য ব্যবস্থাপনা অধিদপ্তরের পরিসংখ্যান কর্মকর্তা - 25.08.2017

419 . $\log_{a} (\frac{m}{n}) = ?$

A. $\log_{a} m - \log_{a} n$
B. $\log_{a} m + \log_{a} n$
C. $\log_{a} m \times \log_{a} n$
D. কোনটিই নয়

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Answer: Option A

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420 . $3 \log^{2} + \log^{5} = ?$

A. log 30
B. log 40
C. 3 log 7
D. log 13

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Answer: Option B

Explanation:

3 \log 2 + \log 5 = \log 2^{3} + \log 5 = \log 8 + \log 5 = \log (8 \times 5) = \log 40

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