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**