Logarithm
 If log 2 = 0.3010, then the number of digits in 2^{64} is ?

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Required answer = [64 log_{10} 2] + 1
Correct Option: C
Required answer = [64 log_{10} 2] + 1
= [ 64 x 0.3010 ] + 1
= 19.264 + 1
= 19 + 1
= 20
 The value of $ \frac{\log_{a}{x}}{\log_{ab}{x}}  \log_{a}{b}$ is ?

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∵ log_{a} x = ( log_{ab}x) / (log_{ab}a)
∴ The given expression = [[(log_{ab}x) / (log_{ab}a)] / [( log_{ab}x )]  ( log_{a}b)
= (1/log_{ab}a)  log_{a}b = log_{a}ab  log_{a}b = log_{a}(ab/b)
= log_{a}a = 1Correct Option: B
∵ log_{a} x = ( log_{ab}x) / (log_{ab}a)
∴ The given expression = [[(log_{ab}x) / (log_{ab}a)] / [( log_{ab}x )]  ( log_{a}b)
= (1/log_{ab}a)  log_{a}b = log_{a}ab  log_{a}b = log_{a}(ab/b)
= log_{a}a = 1
 The value of log_{2}3 x log_{ 3}2 x log_{3}4 x log_{4}3 is ?

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Given Exp.= log_{2}3 x log_{ 3}2 x log_{3}4 x log_{4}3
= (log3 / log2) x ( log2 / log3) x (log4 / log3) x (log3 / log4)Correct Option: A
Given Exp.= log_{2}3 x log_{ 3}2 x log_{3}4 x log_{4}3
= (log3 / log2) x ( log2 / log3) x (log4 / log3) x (log3 / log4) = 1
 Given that log_{10} 2 = 0.3010, then log_{2} 10 is equal to ?

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log_{2} 10 = log 10 / log 2
= 1 / log 2
= 1.0000 / 0.3010Correct Option: C
log_{2} 10 = log 10 / log 2
= 1 / log 2
= 1.0000 / 0.3010
= 1000 / 301
 The value of log 9/8  log 27/32 + log3/4 is ?

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