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Logarithm Test 2
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Logarithm Test 2

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  • Question 1/10
    1 / -0

     

    What is the value of log100 0.1?

    Solutions

    log100 0.1 = log102 

  • Question 2/10
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    If log32 x = 0.8, then x is equal to:

    Solutions

    log32 x = 0.8 Û x = (32)0.8 = (25)4/5 = 24 = 16.

  • Question 3/10
    1 / -0

    If 36 {log6 1/2 + 2log × square root of 2 then x is

    Solutions

    = Applying log on both sides, logx2 × log 36 = log2

    i.e. logx2 = log36 2 ⇒ x = 36

  • Question 4/10
    1 / -0

    The logarithm of a number to a certain base is 9. The logarithm of 64 times the number to a base which is 11 times the original base is 6. Find the original base

    Solutions

    Let the number be x and the base y

    logyX = 9 ⇒ x = y9                                          → (1)

    also, log11y64x = 6 ⇒ 64x = 116 . y6               → (2)

  • Question 5/10
    1 / -0

    What is the value of 2 log (5/8) + log (128/125) + log (5/2)?

    Solutions

    2 log 

    = 2 log 5 – 2 log 8 + log 128 – log 125 + log 5 – log 2

    = 2 log 5 – 2 log 23 + log 27 – log 53 + log 5 – log 2

    = (2 log 5 – 6log 2) + (7 log 2 – 3 log 5) + log 5 – log 2

    = 3 log 5 – 3 log 5 – 7 log 2 + 7 log 2 = 0

  • Question 6/10
    1 / -0

    fraction numerator log space square root of 8 over denominator log space 8 end fraction is equal to:

    Solutions

  • Question 7/10
    1 / -0

    If logy3 x is the same as logx3 y then find the value of logx3y.

    Solutions

    Let logy3x = k ⇒ x = (y3) k = y3k

    Also, logx3y ⇒ y = (x3) k = x3k

    ∴ y = x3k = (y3k) 3k = y9k2   ∴ 9k2 = 1

  • Question 8/10
    1 / -0

    Find the value of square root of a over b end root , if log2(log22(a – b)) = log2 open parentheses square root of straight a minus square root of straight b close parentheses + 1

    Solutions

  • Question 9/10
    1 / -0

    If log x over y + log y over x = log (x + y) then,

    Solutions

  • Question 10/10
    1 / -0

    Which of the following statements is not correct?

    Solutions

    (A) Since loga a = 1, so log10 10 = 1.

    (B) log (2 + 3) = 5 and log (2 × 3) = log 6 = log 2 + log 3

    ∴ log (2 + 3) = log (2 × 3).

    (C) Since loga 1 = 0, so log10 1 = 0.

    (D) log (1 + 2 + 3) = log 6 = log (1 × 2 × 3) = log 1 + log 2 + log 3.

    So, (B) is correct

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