Question 1

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

Accepted Answer

3

Question 2

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 3

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

Question 4

If 5x - 17 = -x + 7, then x = ?

Accepted Answer

Given equation 5x-17 = -x+7 Add 1x to each side of the equation 5x-17+x = -x+7+x 6x=24 x=4

Question 5

If A = log321875 and B = log2432187 , then which one of the following is correct?

Accepted Answer

Given A = log 3 2187 5 a n d B = log 243 2187 B = log 3 5 2187 = log 3 2187 5 => A Therefore, A = B

Question 6

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 7

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 8

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 9

If logaab = x, then logbab = ?

Accepted Answer

x/(x-1)

Question 10

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

Accepted Answer

256/81

Question 11

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 12

Find the logarithm of 144 to the base 23 :

Accepted Answer

log 2 3 144 = 4

Question 13

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

Accepted Answer

1

Question 14

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 15

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 16

The value of 1log360+1log460+1log560is

Accepted Answer

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

Question 17

If log8x = 313 then find the value of x?

Accepted Answer

32

Question 18

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 19

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 20

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

Accepted Answer

Hence the least value of is 4

Logarithm Questions