23
Q:

Find x if 

log1218 = log24x + 1. log24x+1 + 4

A) 0 B) 1
C) 2 D) None of these

Answer:   A) 0



Explanation:

By trial and error method, when we substitute 

x = 0

Both LHS and RHS are equal.

Subject: Logarithms
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Q:

The Value of  logtan10+logtan20++logtan890 is

A) -1 B) 0
C) 1/2 D) 1
 
Answer & Explanation Answer: B) 0

Explanation:

= log tan10+log tan890 + log tan20+ log tan880++log tan450  

 

= log [tan10 × tan890] + log [tan20 × tan880 ] ++log1  

 

 tan(90-θ)=cotθ and tan 450=1  

 

= log 1 + log 1 +.....+log 1 

 

= 0.

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27 5289
Q:

What is the number of digits in 333? Given that log3 = 0.47712?

A) 12 B) 13
C) 14 D) 15
 
Answer & Explanation Answer: B) 13

Explanation:

 Let   Let x=333 333

 

 Then, logx = 33 log3  

 

= 27 x 0.47712 = 12.88224 

 

Since the characteristic in the resultant value of log x is 12

 

The number of digits in x is (12 + 1) = 13 

 

Hence the required number of digits in 333is 13.

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49 9382
Q:

Find value of log27 +log 8 +log1000log 120

A) 1/2 B) 3/2
C) 2 D) 2/3
 
Answer & Explanation Answer: B) 3/2

Explanation:

 = log 33 + log 23+ log 103log10×3×22 

 

 

 

=log33 12+log 23+log 10312log(10×3×22)  

 

 

 

 

 

 

 

=12log 33+3 log 2+12 log103log10+log3+log22  

 

 

 

 

 

 

 

=32log 3 + 2 log 2 + log 10log 3 + 2 log 2 + log 10 = 32  

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27 4686
Q:

The least value of the expression 2log10x - logx1100 for x>1 is:

A) 2 B) 3
C) 4 D) 5
 
Answer & Explanation Answer: C) 4

Explanation:

 

Hence the least value of is 4

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44 6439
Q:

The number of solutions of the equation logx2x2+40log4xx-14log16xx3=0 is:

A) 0 B) 1
C) 2 D) 3
 
Answer & Explanation Answer: D) 3

Explanation:
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14 4118
Q:

If log330 = 1a  and  log530=1b then the value of 3log302 is:

A) 3(1+a+b) B) 2(1-a-b)
C) 3(1-a-b) D) 3(1+a-b)
 
Answer & Explanation Answer: C) 3(1-a-b)

Explanation:
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25 5250
Q:

The greatest possible value of n could be 9n < 108 if, given that log 3 = 0.4771 and nN:

A) 7 B) 8
C) 9 D) 10
 
Answer & Explanation Answer: B) 8

Explanation:

 

Taking Log to both sides 

 we get

 n = 8           

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8 4828
Q:

The value of x satisfying the following relation:

log12x = log23x-2

A) 1/3 B) -1/3
C) 3 D) None of these
 
Answer & Explanation Answer: D) None of these

Explanation:

But at x=-1/3, log x is not defined.

 

The only admissible value of x is 1.

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15 7651