AMCAT Sample Questions Quants Solutions 61- 70

Ques 61 : Choose the correct answer.
What is log-100 ?
Option 1 : 0 Option 2 : 10 Option 3 : 1 Option 4 : Not defined

Log for negative values doesn't exist.

Ques 62 : Choose the correct answer.
What is the value of log3 (-9)?
Option 1 : 3 Option 2 : 1/3 Option 3 : -3 Option 4 : Not defined

Log for negative values doesn't exist.

Ques 63 : Choose the correct answer.
Rajeev multiplies a number by 10, the log (to base 10) of this number will change in what way?
Option 1 : Increase by 10 Option 2 : Increase by 1 Option 3 : Multiplied by 10 Option 4 : None of these

Let the number be x

Let y=y=log10xlog10x
Now, 10x;
log10 10x=log1010+log10xlog1010x=log1010+log10x
Since,
logxab=logxa+logxblogxab=logxa+logxb
loga a=1loga a=1
Hence
log10 10x=1+log10xlog10 10x=1+log10x
log101 0x=1+y

Ques 64 : Choose the correct answer.
The logarithm of a very small positive number will tend to which of the following?
Option 1 : 0 Option 2 : negative infinity Option 3 : positive infinity Option 4 : 1

Ques 65 : Choose the correct answer.
If n numbers are in geometric progression, the logarithm of the number will be in which of the following?
Option 1 : Geometric Progression Option 2 : Arithmetic Progression Option 3 : Harmonic Progression Option 4 : None of these

Explanation : a,b,c are in GP ba=cbba=cb
b2=acb2=ac
logarithm on both sides
log(b2)=log(ac)log(b2)=log(ac)
2logb=loga+logc=logb+logb2logb=loga+logc=logb+logb
logb−loga=logc−logblogb−loga=logc−logb
Therefore , loga,logb,logcareinAP.

Ques 66 : Choose the correct answer.
Which of the following is equivalent to log(a + b) ?
Option 1 : log a + log b Option 2 : log a * log b Option 3 : log a - log b Option 4 : None of these

Ques 67 : Choose the correct answer.
What is the value of log3 (1/9) + log 9 81 ?
Option 1 : 2 Option 2 : -2 Option 3 : 0 Option 4 : 4

Ques 68 : Choose the correct answer.
What is the value of log3 1.5 + log3 6 ?
Option 1 : 2 Option 2 : 2.7 Option 3 : 1.8 Option 4 : None of these
log3 1.5+ log3 6
=log3(1.5*6)
=log9
=log3^2
=2*log3 3
=2 ans

Ques 69 : Choose the correct answer.
Which of the following is log8 x equivalent to?
Option 1 : log2 (x/3) Option 2 : log2 (3x) Option 3 : (log2x)/ 3 Option 4 : None of these

Ques 70 : Choose the correct answer.
If n numbers are in arithmetic progression, the logarithm of the number will be in which of the following?
Option 1 : Exponentially Option 2 : Linearly Option 3 : Quadratically Option 4 : None of these

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