Question 1

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

Accepted Answer

Hence the least value of is 4

Question 2

Solve the equation 122x+1 = 1 ?

Accepted Answer

Rewrite equation as 1 2 2 x + 1 = 1 2 0 Leads to 2x + 1 = 0 Solve for x : x = -1/2

Question 3

For x∈N, x>1 , and p=logxx+1 , q=logx+1x+2 then which one of the following is correct?

Accepted Answer

k l > k + 1 l + 1 for (k,l) > 0 and k > l Let k = x+1 and l = x Therefore, x + 1 x > ( x + 1 ) + 1 ( x ) + 1 (x + 1) > x Therefore, log ( x + 1 ) log ( x ) > log ( x + 2 ) log ( x + 1 ) ⇒ log x x + 1 > log x + 1 x + 2

Question 4

if log105+log5x+1=log10(x+5)+1,then x is equal to

Accepted Answer

log 10 5 + log 5 x + 1 = log 10 x + 5 + 1 log 10 5 5 x + 1 = log 10 10 x + 5 5 5 x + 1 = 10 x + 5 5x+1=2x+10 3x=9 x=3

Question 5

What is the characteristic of the logarithm of 0.0000134?

Accepted Answer

log (0.0000134). Since there are four zeros between the decimal point and the first significant digit, the characteristic is –5.

Question 6

Find value of log27 +log 8 +log1000log 120

Accepted Answer

= log 3 3 + log 2 3 + log 10 3 log 10 × 3 × 2 2 = log 3 3 1 2 + log 2 3 + log 10 3 1 2 log ( 10 × 3 × 2 2 ) = 1 2 log 3 3 + 3 log 2 + 1 2 log 10 3 log 10 + log 3 + log 2 2 = 3 2 log 3 + 2 log 2 + log 10 log 3 + 2 log 2 + log 10 = 3 2

Question 7

The Value of logtan10+logtan20+⋯⋯+logtan890 is

Accepted Answer

= log tan 1 0 + log tan 89 0 + log tan 2 0 + log tan 88 0 + ⋯ ⋯ + log tan 45 0 = log [ tan 1 0 × tan 89 0 ] + log [ tan 2 0 × tan 88 0 ] + ⋯ ⋯ + log 1 ∵ tan ( 90 - θ ) = c o t θ a n d tan 45 0 = 1 = log 1 + log 1 +.....+log 1 = 0.

Question 8

The value of 13log10125 - 2log104 + log1032 :

Accepted Answer

1

Question 9

If a2+b2 = c2 , then 1logc+ab + 1logc-ab = ?

Accepted Answer

Given a 2 + b 2 = c 2 Now 1 log c + a b + 1 log c - a b = log b c + a + log b c - a = log b c 2 - a 2 = 2 log b b = 2

Question 10

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

Accepted Answer

3(1-a-b)

Question 11

Which of the following statements is not correct?

Accepted Answer

log (2 + 3) = log 5 log (2 x 3) = log 2 + log 3 log (2 + 3) ≠ log (2 x 3)

Question 12

Find x if log1218 = log24x + 1. log24x+1 + 4

Accepted Answer

By trial and error method, when we substitute x = 0 Both LHS and RHS are equal.

Question 13

The value of log55log49log32 is :

Accepted Answer

1

Question 14

It is given that log10 2= 0.301 and log10 3 = 0.477. How many digits are there in (108)10 ?

Accepted Answer

21

Question 15

The value of x satisfying the following relation: log12x = log23x-2

Accepted Answer

But at x=-1/3, log x is not defined. The only admissible value of x is 1.

Question 16

The value of log2log5625 is :

Accepted Answer

2

Question 17

If a = bx, b = cy and c = az then the value of xyz is equal to :

Accepted Answer

1

Question 18

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

Accepted Answer

3

Question 19

If a, b, c be the pth, qth and rth terms of a GP then the value of (q-r) log a + (r-p) log b + (p-q) log c is :

Accepted Answer

Question 20

The value of log3437 is :

Accepted Answer

log 343 7 log 7 3 7 1 3 log 7 7 W e k n o w t h a t l o g x x = 1 = > 1 3

Logarithm Questions