# 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

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

Explanation:

 log2 10 = 1 = 1 = 10000 = 1000 . log10 2 0.301 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

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

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