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- Total Questions 20
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1. log 32700 = ?

Correct Answers :

[A]

Explanation :

Log 32700 = log 3.27 + log 10000 = log 3.27 + 4

2. log . 0867 = ?*x*

Correct Answers :

[B]

Explanation :

Log 0.0867 = log (8.67/100) = log 8.67 – log 100

Log 8.67 – 2

3. If log_{10}^{2} = .301 find log_{10}125.

Correct Answers :

[A]

Explanation :

log_{10} 125 = log_{10}(1000/8) = log.1000 – 3log2

= 3 – 3 × 0.301 = 2.097

4. log_{32} 8 = ?

Correct Answers :

[C]

Explanation :

log32 8 = log 8/log 32 (By base change rule)

= 3 log2/5log2 = 3/5.

5. Find the value of x, log_{0.5}x = 25

Correct Answers :

[A]

Explanation :

log_{0.5} x = 25 fi x = 0.5^{25} = (1/2)^{25} = 2^{-25}

6. Find the value of x, log_{3}x = 1/2

Correct Answers :

[B]

Explanation :

x = 3^{1/2} = √3 .

7. log_{15}3375 × log_{4}1024 = ?

Correct Answers :

[D]

Explanation :

log_{15}3375 × Log_{4}1024
= 3 log_{15} 15 × 5 log_{4} 4 = 3 × 5 = 15.

8. log_{a}4 + log_{a}16 + log_{a}64 + log_{a}256 = 10. Then a = ?

Correct Answers :

[A]

Explanation :

The given expression is:

Loga (4 × 16 × 64 × 256) = 10

i.e.log_{a} 4_{10} = 10

Thus, a = 4.

9. log_{625}√5 = ?

Correct Answers :

[C]

Explanation :

1/2 log_{625} 5 = [1/(2 × 4)] log_{5} 5 = 1/8.

10. If log x + log (x + 3) = 1 then the value(s) of x will be, the solution of the equation

Correct Answers :

[C]

Explanation :

log x (x + 3) = 1 fi 10^{1} = x^{2} + 3x.

or x(x + 3) = 10.

11. If log_{10}a = b, find the value of 10^{3b} in terms of a.

Correct Answers :

[A]

Explanation :

log_{10} a = b fi 10^{b} = a fi By definition of logs.
Thus 10^{3b} = (10^{b})^{3} = a^{3}.

12. 3 log 5 + 2 log 4 – log 2 = ?

Correct Answers :

[B]

Explanation :

3 log 5 + 2 log 4 – log 2

= log 125 + log 16 – log 2

= log (125 × 16)/2 = log 1000 = 3.

13. Solve equations, for the value of x, log (3x – 2) = 1

Correct Answers :

[C]

Explanation :

10^{1} = 3x – 2 fi x = 4.

14. Solve equations, for the value of x, log (2x – 3) = 2

Correct Answers :

[B]

Explanation :

10^{2} = 2x – 3 fi x = 51.5

15. Solve equations, for the value of x, log (12 – x) = –1

Correct Answers :

[D]

Explanation :

1/10 = 12 – x fi x = 11.9

16. Solve equations, for the value of x, log (x^{2} – 6x + 6) = 0

Correct Answers :

[C]

Explanation :

x^{2} – 6x + 6 = 10° fi x^{2} – 6x + 6 = 1

fi x^{2} – 6x + 5 = 0

Solving gives us x = 5 and 1.

17. Solve equations, for the value of x, log 2^{x} = 3

Correct Answers :

[C]

Explanation :

x log 2 = 3

log 2 = 3/x.

Therefore, x = 3/log 2

18. Solve equations, for the value of x, 3^{x} = 7

Correct Answers :

[A]

Explanation :

3^{x} = 7 fi log_{3} 7 = x
Hence x = 1/log_{7} 3

19. Solve equations, for the value of x, 5^{x} = 10

Correct Answers :

[D]

Explanation :

x = log_{5} 10 = 1/log_{10} 5 = 1/log 5.

20. Find x, if 0.01^{x} = 2

Correct Answers :

[D]

Explanation :

x = log_{0.01} 2 = –log 2/2.

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