Logarithm
- If log 2 = 0.3010, then the number of digits in 264 is ?
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Required answer = [64 log10 2] + 1
Correct Option: C
Required answer = [64 log10 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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∵ loga x = ( logabx) / (logaba)
∴ The given expression = [[(logabx) / (logaba)] / [( logabx )] - ( logab)
= (1/logaba) - logab = logaab - logab = loga(ab/b)
= logaa = 1Correct Option: B
∵ loga x = ( logabx) / (logaba)
∴ The given expression = [[(logabx) / (logaba)] / [( logabx )] - ( logab)
= (1/logaba) - logab = logaab - logab = loga(ab/b)
= logaa = 1
- The value of log23 x log 32 x log34 x log43 is ?
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Given Exp.= log23 x log 32 x log34 x log43
= (log3 / log2) x ( log2 / log3) x (log4 / log3) x (log3 / log4)Correct Option: A
Given Exp.= log23 x log 32 x log34 x log43
= (log3 / log2) x ( log2 / log3) x (log4 / log3) x (log3 / log4) = 1
- Given that log10 2 = 0.3010, then log2 10 is equal to ?
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log2 10 = log 10 / log 2
= 1 / log 2
= 1.0000 / 0.3010Correct Option: C
log2 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