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 & Explanation
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 & Explanation
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 & Explanation
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 & Explanation
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 & Explanation
Answer: Option B
Explanation:
Given expression = log60 3 + log60 4 + log60 5
= log60 (3 x 4 x 5)
= log60 60
= 1.