








1.

What is the value of 2 log 
( 
5 
) 
+ log 
( 
128 
) 
+ log 
( 
5 
) 
? 
8 
125 
2 

Answer: Option
A
Explanation:
= 2 log 
( 
5 
) 
+ log 
( 
128 
) 
+ log 
( 
5 
) 
8 
125 
2 
= log 
( 
5 
) 
^{2} 
+ log 
( 
128 
) 
+ log 
( 
5 
) 
8 

125 
2 
= log 
( 
5^{2} × 128 × 5 
) 
^{2} 
= log 
( 
5^{2} × 2^{7} × 5 
) 
8^{2} × 125 × 2 

(2^{3})^{2} × 5^{3} × 2 
= log 
( 
2^{7} × 5^{3} 
) 
^{2} 
= log 
( 
2^{7} × 5^{3} 
) 
2^{6} × 5^{3} × 2 

2^{7} × 5^{3} 
= log 1 = 0.


2.

What is the value of log_{100} 0.1?

Answer: Option
B
Explanation:
log_{100} 0.1 = log_{100 } 
1 
10 
= log _{100} 1 – log _{10}2 10
= 0 – 
1 
log_{10} 10 = – 
1 
× 1 = – 
1 
. 
2 
2 
2 


3.

What is the value of 
[log_{13} (10)] 
? 
log_{169} (10)] 

Answer: Option
B
Explanation:
[log_{13} (10)] 
= 
log_{13} (10) 

(∴ log_{a}b (C) = 
1 
log_{a} C) 
log_{169} (10)] 
log_{13}2 (10) 
b 


4.

What is the logarithm of 0.0001 with respect to base 10?

Answer: Option
C
Explanation:
Let log _{10} 0.0001 = x
⇒ x = log _{10} (10) ^{–4}
⇒ log _{10} 1 – log _{10} (10) ^{4} = 0 – 4 = – 4.


5.

What is the value of 
1 
log_{10} 25 – 2log_{10} 3 + log_{10} 18? 
2 

Answer: Option
C
Explanation:
1 
log_{10} 25 – 2log_{10} 3 + log_{10} 18 
2 
= log _{10} 25 ^{1/2} – log _{10} 3 ^{2} + log _{10} 18
= log _{10} 5 – log _{10} 9 + log _{10} 18
= log_{10} 
5 × 18 
= log_{10} 
90 
= log_{10} 10 = 1 
9 
9 






