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Quiz – 1

June 23, 2019

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Question 1

Time: 00:00:00

If a^x = b^y, then

log a/b= x/y

log a/ log b = x/y

log a/ log b = y/x

log a/b= y/x

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(c). a^x = b^y => log a^x = log b^y => x log a = y log b

=> log a/ log b = y/x

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Question 2

Time: 00:00:00

2 log₁₀ 5 + log₁₀ 8 – ½ log₁₀ 4 = ?

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(a). 2 log₁₀ 5 + log₁₀ 8 – ½ log₁₀ 4

= log₁₀ (5²) + log₁₀ 8 - log₁₀ (4^1/2)

= log₁₀ 25 + log₁₀8 - log₁₀ 2 = log₁₀(25*8)/2

= log₁₀ 100 = 2

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Question 3

Time: 00:00:00

log_a (ab) = x, then log _b (ab) is :

1/x

x/ (x+1)

x/(1-x)

x/(x-1)

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(d). log_a (ab) = x => log b/ log a = x => (log a + log b)/ log a = x

1+ (log b/ log a) = x => log b/ log a = x-1

log a/ log b = 1/ (x-1) => 1+ (log a/ log b) = 1 + 1/ (x-1)

(log b/ log b) + (log a/ log b) = x/ (x-1) => (log b + log a)/ log b = x/ (x-1)

=>log (ab)/ log b = x/(x-1) => log_b (ab) = x/(x-1)

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Question 4

Time: 00:00:00

If log_xy = 100 and log₃x = 10, then the value of y is:

3 ^1000

3^ 10000

3^10

3^ 100

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ANSWER: 3¹⁰⁰⁰

Explanation:
log₃x = 10
Hence,x= 3¹⁰
log_x y = 100
y =x¹⁰⁰ = (3¹⁰)¹⁰⁰= y = 3¹⁰⁰⁰

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Question 5

Time: 00:00:00

If log 2 = 0.3010, then the number of digits in 2⁶⁴ is ?

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Correct Option: C

Required answer = [64 log₁₀ 2] + 1
= [ 64 x 0.3010 ] + 1
= 19.264 + 1
= 19 + 1
= 20

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Question 6

Time: 00:00:00

The value of log₂3 x log₃2 x log₃4 x log₄3 is ?

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Correct Option: A

Given Exp.= log₂3 x log₃2 x log₃4 x log₄3
= (log3 / log2) x ( log2 / log3) x (log4 / log3) x (log3 / log4) = 1

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Question 7

Time: 00:00:00

Given that log₁₀ 2 = 0.3010, then log₂ 10 is equal to ?

22/445

103/456

1000/301

12/45

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Correct Option: C

log₂ 10 = log 10 / log 2
= 1 / log 2
= 1.0000 / 0.3010
= 1000 / 301

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Question 8

Time: 00:00:00

The value of log 9/8 - log 27/32 + log3/4 is ?

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Correct Option: A

Given Exp. = log [{(9/8) / (27/32)} x 3/4)]
= log [(9/8) x (3/4) x (32/27)]
= log 1
= 0

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Question 9

Time: 00:00:00

The simplified form of log(75/16) -2 log(5/9) +log(32/343) is ?

log 2

log 4

log 8

log 10

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Correct Option: A

Given Exp. = log75/16 - 2 log5/9 + log32/343
= log [(25 x 3) / (4 x 4)] - log (25/81) + log [(16 x 2) / (81 x 3)]
= log(25 x 3) - log ( 4 x 4 ) - log(25) + log81 + log(16 x 2) -log (81 x 3)
= log 25 + log 3 - log 16 - log 25 + log 81 + log 16 + log 2 - log 81 - log 3
= log 2

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Question 10

Time: 00:00:00

If log 2 = 0.3010 then log 5 equals to ?

0.3010

0.6990

0.7525

None

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Correct Option: B

log 5 = log 10 /2 = log 10 - log 2
= 1 - 0.3010 = 0.6990

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["0","40","60","80","100"]

["Need more practice!","Keep trying!","Not bad!","Good work!","Perfect!"]

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