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March 30, 2017

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Find the value of the following.

10^(-10log3)

The log exponent is confusing me. Could someone please help me? Thanks.

  • Math - ,

    -10log3= log3^-10= log (1/3^10)

    so 10^(log(1/3^10)= 1/3^10

    Here is an unconfusing explanation.

    log100=2
    so 10^2=l0^(log100) by definition.

  • Math - ,

    Have you come across the property of logs that says ..

    a^loga k = k

    your question fits that pattern after a quick adjustment

    10^(-10log3)
    = 10^(log 3^(-10))
    = 3^-10
    = 1/3^10 , so far no calculator
    = appr. .000016935

    check:
    log3 = .47771213
    -10log3 = -4.771213
    10^-4.771213 = .00016935

  • Math - ,

    Thanks!

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