Question 1

A fast moving superfast express crosses another pasenger train in 20 seconds. The speed of faster train is 72 km/hr and speeds of slower train is 27 km/h. Also the length of faster ntrain is 100m, then find the length of the slower train if they are…

Accepted Answer

T i m e = S u m o f l e n g t h o f t h e t w o t r a i n s D i f f e r e n c e i n s p e e d s 20 = ( 100 + x ) 25 2 ⇒ X=150m

Question 2

The value of 1log360+1log460+1log560is

Accepted Answer

=> log 60 ( 3 * 4 * 5 ) => log 60 60 = 1

Question 3

If log8x = 313 then find the value of x?

Accepted Answer

32

Question 4

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

Accepted Answer

Let L e t x = 3 3 3 = 3 3 3 Then, log x = 3 3 log 3 = 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 3 3 3 is 13.

Question 5

if logab+logba=loga+b,then

Accepted Answer

i f log a b + log b a = log a + b , t h e n log a + b = log a b × b a = log 1 so, a+b=1

Question 6

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

Accepted Answer

Hence the least value of is 4

Question 7

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 8

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 9

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 10

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 11

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 12

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 13

The value of 13log10125 - 2log104 + log1032 :

Accepted Answer

1

Question 14

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 15

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

Accepted Answer

3(1-a-b)

Question 16

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 17

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 18

The value of log55log49log32 is :

Accepted Answer

1

Question 19

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 20

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.

Logarithm Questions