Aptitude - Logarithm

Exercise :: Logarithm - General Questions

6. 

If log10 7 = a, then log10 1 is equal to:
70

A. - (1 + a)
B. (1 + a)-1
C.
a
10
D.
1
10a

Answer: Option A

Explanation:

log10 1
70
= log10 1 - log10 70
= - log10 (7 x 10)
= - (log10 7 + log10 10)
= - (a + 1).

7. 

If log10 2 = 0.3010, then log2 10 is equal to:

A.
699
301
B.
1000
301
C. 0.3010
D. 0.6990

Answer: Option B

Explanation:

log2 10 = 1 = 1 = 10000 = 1000 .
log10 2 0.3010 3010 301

8. 

If log10 2 = 0.3010, the value of log10 80 is:

A. 1.6020
B. 1.9030
C. 3.9030
D. None of these

Answer: Option B

Explanation:

log10 80 = log10 (8 x 10)
= log10 8 + log10 10
= log10 (23 ) + 1
= 3 log10 2 + 1
= (3 x 0.3010) + 1
= 1.9030.

9. 

If log10 5 + log10 (5x + 1) = log10 (x + 5) + 1, then x is equal to:

A. 1
B. 3
C. 5
D. 10

Answer: Option B

Explanation:

log10 5 + log10 (5x + 1) = log10 (x + 5) + 1

log10 5 + log10 (5x + 1) = log10 (x + 5) + log10 10

log10 [5 (5x + 1)] = log10 [10(x + 5)]

5(5x + 1) = 10(x + 5)

5x + 1 = 2x + 10

3x = 9

x = 3.


10. 

The value of 1 + 1 + 1 is:
log3 60 log4 60 log5 60

A. 0
B. 1
C. 5
D. 60

Answer: Option B

Explanation:

Given expression = log60 3 + log60 4 + log60 5
= log60 (3 x 4 x 5)
= log60 60
= 1.