Logarithm

  1. If log 2 = 0.3010, then the number of digits in 264 is ?
    1. 18
    2. 19
    3. 20
    4. 21
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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

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  1. The value of $ \frac{\log_{a}{x}}{\log_{ab}{x}} - \log_{a}{b}$ is ?
    1. 0
    2. 1
    3. a
    4. ab
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    ∵ loga x = ( logabx) / (logaba)
    ∴ The given expression = [[(logabx) / (logaba)] / [( logabx )] - ( logab)
    = (1/logaba) - logab = logaab - logab = loga(ab/b)
    = logaa = 1

    Correct Option: B

    ∵ loga x = ( logabx) / (logaba)
    ∴ The given expression = [[(logabx) / (logaba)] / [( logabx )] - ( logab)
    = (1/logaba) - logab = logaab - logab = loga(ab/b)
    = logaa = 1

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  1. The value of log23 x log 32 x log34 x log43 is ?
    1. 1
    2. 2
    3. 3
    4. 4
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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

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  1. Given that log10 2 = 0.3010, then log2 10 is equal to ?
    1. 0.3010
    2. 0.6990
    3. 1000 / 301
    4. 699 / 301
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    log2 10 = log 10 / log 2
    = 1 / log 2
    = 1.0000 / 0.3010

    Correct Option: C

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

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  1. The value of log 9/8 - log 27/32 + log3/4 is ?
    1. 0
    2. 1
    3. 2
    4. 3
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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

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