Question 1

If log 2 = 0.3010 and log 3 = 0.4771, the values of log5 512 is

Accepted Answer

ANS: log5512 = log512/log5 = log 2 9 log 10 / 2 = 9 log 2 log 10 - log 2 = 9 * 0 . 3010 1 - 0 . 3010 =2.709/0.699 =2709/699 =3.876

Question 2

If log 2 = 0.30103, Find the number of digits in 256 is

Accepted Answer

log ( 2 56 ) =56*0.30103 =16.85768. Its characteristics is 16. Hence, the number of digits in 2 56 is 17.

Question 3

If log 27 = 1.431, then the value of log 9 is

Accepted Answer

log 27 = 1.431 log 3 3 = 1.431 3 log 3 = 1.431 log 3 = 0.477 log 9 = log( 3 2 )= 2 log 3 = (2 x 0.477) = 0.954

Question 4

If logaab = x, then logbab = ?

Accepted Answer

x/(x-1)

Question 5

If logx916 = -12, then the value of x?

Accepted Answer

256/81

Question 6

If log72 = m, then log4928 is equal to ?

Accepted Answer

log 49 28 = 1 2 log 7 7 × 4 = 1 2 + 1 2 2 log 7 2 = 1 2 + log 7 2 = 1 2 + m = 1 + 2 m 2 .

Question 7

Find the logarithm of 144 to the base 23 :

Accepted Answer

log 2 3 144 = 4

Question 8

If logxl+m-2n = logym+n-2l = logzn+l-2m , then xyz is equal to

Accepted Answer

1

Question 9

If log 64 = 1.8061, then the value of log 16 will be (approx)?

Accepted Answer

Given that, log 64 = 1.8061 i.e log 4 3 = 1 . 8061 --> 3 log 4 = 1.8061 --> log 4 = 0.6020 --> 2 log 4 = 1.2040 ⇒ log 4 2 = 1 . 2040 Therefore, log 16 = 1.2040

Question 10

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 11

If log8x = 313 then find the value of x?

Accepted Answer

32

Question 12

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 13

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 14

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 15

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 16

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 17

The value of 13log10125 - 2log104 + log1032 :

Accepted Answer

1

Question 18

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

Accepted Answer

3(1-a-b)

Question 19

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 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