Practice Question on Logarithms for IITJEE , NDA And Airforce 16-30

Logarithms

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Question no. 16

The value of

looks_one 1

looks_two 4

looks_3 2

looks_4 3

Option looks_one 1

Solution :

Question no. 17

If log₄7 = x, then log₇ 16 is equal to

looks_one 2/x

looks_two x

looks_3 x²

looks_4 2x

Option looks_one 2/x

Solution :
log₄7 = x
1/log₇4 = x
1/log₇(16)^1/2 = x
2/log₇(16) = x
log₇(16) = 2/x

Question no. 18

If n=2017! then is

looks_one 0

looks_two 1

looks_3 n/2

looks_4 n

Option looks_two 1

Solution :

Question no. 19

log(ab)-log|b|=

looks_one log a

looks_two log|a|

looks_3 -loga

looks_4 none of these

Option looks_two log|a|

Solution :
log(ab)-log|b| = log |ab/ b| = log|a|

Question no. 20

If log₄5=a and log₅6=b , then log₃2 is equal to

looks_one 1/(2a+1)

looks_two 1/(2b+1)

looks_3 2ab+1

looks_4 1/(2ab-1)

Option looks_4 1/(2ab-1)

Solution :

Question no. 21

If log₁₂27=b , then log₆ 16=

looks_one 2(3-b)/(3+b)

looks_two 3(3-b)/(3+b)

looks_3 4(3-b)/(3+b)

looks_4 none of these

Option looks_3 4(3-b)/(3+b)

Solution :

Question no. 22

log₄18 is

looks_one a rational number

looks_two an irrational number

looks_3 a prime number

looks_4 none of these

Option looks_two an irrational number

log₄18 gives an irrational number

Question no. 23

If B=log₂ log₂ log₄ 256 +2 log_√2 2, then B is equal to

looks_one 2

looks_two 3

looks_3 5

looks_4 7

Option looks_3 5

Solution :
2 log_√2 2 = 2log_√2 √2 = 4
log₂ log₂ log₄ 256 = log₂ log₂log₄4⁴
log₂ log₂4 = log₂2 = 1
2 log_√2 2 + log₂ log₂ log₄ 256 = 4 + 1 = 5

Question no. 24

If a^x=b, b^y=c, c^z=a, then the value of xyz is

looks_one 0

looks_two 1

looks_3 2

looks_4 3

Option looks_two 1

Solution :

Question no. 25

If log ₁₀x=y, then log₁₀₀₀x² is

looks_one 2y

looks_two 2y/3

looks_3 3y/2

looks_4 y²

Option looks_two 2y/3

Solution :
log ₁₀x=y
log₁₀₀₀x² = (2/3)log ₁₀x = (2/3)y

Question no. 26

if x=log₅(1000) and y=log₇(2058) then

looks_one x=y

looks_two x<(y)

looks_3 x>y

looks_4 none of these

Option looks_3 x>y

Solution :
x= log₅(1000) has 5 digit :
log₅(625) < log₅(1000) < log₅(3125)
4 < log₅(1000) < 5
y=log₇(2058) has 4 digit :
log₇(343) < log₇(2058) < log₇(2401)
3 < log₇(2058) < 4

Question no. 27

the value of (0.05)^{log_√20(0.1 +0.01 +.001 +......)}

looks_one 81

looks_two 1/81

looks_3 20

looks_4 1/20

Option looks_one 81

Solution :

Question no. 28

The value of 81^(1/log₅3) +27^(log₉36) +3^(4/log₇9)

looks_one 49

looks_two 625

looks_3 216

looks_4 890

Option looks_4 890

Solution :
81^(1/log₅3) +27^(log₉36) +3^(4/log₇9)
81^(log₃5) +27^(log₉36) +3^(4log₉7)
3^(4log₃5) +3^{((3/2)log₃62)} +3^{((4/2)3log₃7)}
3^(log₃54) +3^(log₃63) +3^(3log₃72)
5⁴ + 6 ³ + 7² = 890

Question no. 29

If log_kx.log₅k=log_x5, k≠1,k>0, then x is equal to

looks_one k

looks_two 1/5

looks_3 5

looks_4 5 and 1/5

Option looks_4 5 and 1/5

Solution :

Question no. 30

If log₁₀2=0.30103 , log₁₀3=0.47712 , the number of digits in 3¹².2⁸ is

looks_one 7

looks_two 8

looks_3 9

looks_4 10

Option looks_3 9

Solution :
3¹².2⁸
take log with base 10
log₁₀3¹².2⁸
log₁₀3¹² + log₁₀2⁸
12 * 0.477 + 8 *0.3 = 8.133
there are 9 digits in mumber

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