Practice question on logarithms for iit-jee , NDA and airforce

Logarithms

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Question no. 1

If log₂ x = 4, then x is equal to

looks_one 16

looks_two 4

looks_3 2

looks_4 64

Option looks_one 16

log₂x = 4
x = 2⁴
x = 16

Question no. 2

1f (log₃x)² + (log₃x) < 2, then which one of the following is correct?

looks_one 0<(x)< 1/9

looks_two 1/9<(x)<3

looks_3 3< (x) <∞

looks_4 1/9 ≤x≤3

Option looks_two 1/9<(x)<3

(log₃x)² + (log₃x) < 2
let log₃x = Y
Y² + Y < 2
Y² + Y - 2 < 0
(Y-1) (Y+2) < 0
Y = (-2,1)
-2 > log₃x < 1
1/9 > x < 3

Question no. 3

What is the value of log_b^1/2a . log_c^1/3b . log_a^1/4c?

looks_one 12

looks_two 24

looks_3 1/12

looks_4 1/24

Option looks_two 24

log_b^1/2a . log_c^1/3b . log_a^1/4c

Question no. 4

If (logx/log5)=(log36/log6)=(log64/logy), what are the values of x and y respectively?

looks_one 8,25

looks_two25,8

looks_3 8,8

looks_4 25,25

Option looks_two25,8

Question no. 5

What is the number of digits in the numeral form of 8¹⁷?

looks_one 51

looks_two 16

looks_3 15

looks_4 14

Option looks_two 16

Take log₁₀
17log₁₀8 = 17 * 3log₁₀2
51 * 0.301 = 15. 351
This is 15 zeros digit , So number of digits is 16

Question no. 6

Find the value of x in log256/log16=log x

looks_one 1

looks_two 10

looks_3 100

looks_4 1000

Option looks_3 100

Question no. 7

What is the value of log₁₀5 + log₁₀(5x + 1) = log₁₀(x + 5) +1, then x is equal to?

looks_one 1

looks_two 3

looks_3 5

looks_4 10

Option looks_two 3

log₁₀5 + log₁₀(5x + 1) = log₁₀(x+5) + 1
log₁₀5 - log₁₀10 = log₁₀(x+5) - log₁₀(5x + 1)
log₁₀(1/2) = log₁₀(x+5)/(5x+1)
1/2 = (x+5)/(5x+1)
5x + 1 = 2x + 10
3x = 9
x =3

Question no. 8

Express 81^1/4 = 3 in terms of logarithm.

looks_one log₈₁3=1/4

looks_two log_1/43 = 81

looks_3 log₈₁(1/4) =3

looks_4 None of these

Option looks_one log₈₁3=1/4

81^1/4 = 3
1/4 = log₈₁3

Question no. 9

What is the value of ?

looks_one 0

looks_two 1

looks_3 2

looks_4 1/2

Option looks_one 0

Question no. 10

The value of log₃4.log ₄5.log₅6.log₆7.log₇8.log₈9 is

looks_one 1

looks_two 2

looks_3 1/2

looks_4 3

Option looks_two 2

Question no. 11

For what non-negative integers a, b and c, what would be the value of a + b + c, if log a + log b + log c = 0

looks_one 3

looks_two 1

looks_3 0

looks_4 -1

Option looks_one 3

log a + log b + log c = 0
log abc = 0
abc = 1
( a + b + c ) / 3 ≥ ³√abc
a + b + c ≥ 3

Question no. 12

If log₁₀2 = 0.3010, then what is the number of digits in 20¹⁶?

looks_one 19

looks_two 20

looks_3 21

looks_4 none of these

Option looks_3 21

20¹⁶
16log₁₀20
16 [log₁₀2 + 1]
16 [.301 + 1]
20.8 [it means it has 20 zeros after a digit]
So it has 21 digits

Question no. 13

Find the value of , given that log 2 = 0.3010 and log 3=0.4771

looks_one 0.3010

looks_two 0.3512

looks_3 0.412

looks_4 none of these

Option looks_one 0.3010

Question no. 14

What is the value of ?

looks_one 1

looks_two 2

looks_3 4

looks_4 8

Option looks_3 4

Question no. 15

If a = log 2, b = log 3, c = log 7, and 6^x = 7^x+4, then find x.

looks_one 4b/(a-b+c)

looks_two 4c/(a+b-c)

looks_3 4b/(-a-b+c)

looks_4 4b/(a+b-c)

Option looks_two 4c/(a+b-c)

a = log 2 , b =log 3 , c = log 7
6^x = 7^x+4 [take log both sides]
x log 6 = (x+4)log 7
x (log 2 + log 3) = (x+4) c
x(a + b) = (x+ 4)c
x = 4c /(a+b-c)

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