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Precalculus

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PLEASE HELP ME WITH THESE QUESTION AS MUCH AS POSSIBLE!!
Evaluate without a calculator. Give exact answers:
a) log(log(10)) = ?
b) square root (log(100)) - log(square root(100)) = ?
c) log((square root 10^3)(square root 10^5)(square root 10) = ?
d) 1000^log(3) = ?
e) log(1/log(10square root 10)) = ?

  • Precalculus - ,

    a) log(log10)
    = log 1 = 0

    b) √log100 - log(√100)
    = √2 - log10
    =√2 - 1

    c) log(√10^3√10^5√10)
    = log √10^9
    = log 10^(9/2)
    = (9/2)log10 = (9/1)(1) = 9/2

    d) 1000^log3
    = ((10)^3)^log3
    = 10 ^(3log3)
    = 10^(log27)
    = 27

    e) log (1/log(10√10)
    = log 1 - log(10√10)
    = 0 - log(10√10)
    = -log(10√10)
    = -(log10 + log(√10)
    = -(1 + 1/2_
    = -3/2

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