Page 38 - Mathematics Class - XII

Viva-Voce

1. Define natural logarithms.
Ans. Logarithms to the base e are called Naperian logarithms or natural logarithms.

2. What are common logarithms?
Ans. Logarithms to the base 10 are called common logarithms.
3. What is the nature of e?
Ans. The number e is an irrational number. The value of e is approximately equal to 2.7182818 (which is
rounded to 7 decimal digits).
4. What is the value of log e ?
e
Ans. log e = 1 because e = e.
1
e
5. What is the nature of the graph of f (x) = log x, where 0 < a < 1?
a
Ans. The function f (x) = log x, for 0 < a < 1 has a graph which is close to the positive f (x)-axis for x < 1 and
a
decreases slowly for positive x.
6. What is the relation between natural log and common log?
Ans. Natural log = 2.303 × Common log.

MCQs

1. If 2 = 32, then x = ?
x
a) 2 b) 3 c) 4 d) 5

2. If a = b , then y = ?
y
a) log a b) log b c) log x d) log x
b a a b
1
3. The value of the log 10 is
100
a) –2 b) 2 c) –5 d) 5

1
4. The value of x in equation log x = 4 is
81
1 1
a) 2 b) c) 3 d) 3
2
5. (log xy) (log x ) = ?
y
x xy
a) x b) y c) x y d) y x
6. log 4 + log 25 = ?
a) 2 b) 3 c) 4 d) 5

7. What is the value of x in equation log (x + 2) – log (x – 1) = log 2
a) 2 b) 3 c) 4 d) 5
1
Answers: 1. d) 5 2. a) log a 3. a) –2 4. d) 5. b) y 6. a) 2 7. c) 4
3
b
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