Logarithms

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I need help evaluation the following:

1.) (1/15)^2.309

It says hint: set the expression = x and take the logs of both sides.

I did: x=(1/15)^2.309
logx = log(1/15)^2.309 = 2.309 log(1/15)
and I don't know how to proceed or if I'm on the right track.

2.) Find the base x for which
logx (4.44 * 10^4) = 4.44

Hint: write the corresponding exponential expression.

I did 4.44^x = (4.44 * 10^4)

  • Logarithms -

    logx = log(1/15)^2.309 = 2.309 log(1/15)
    so far ok

    log x = 2.309(-1.17609...)
    = -2.71559..

    now press the following on your calculator
    2ndF or INV
    log
    =.001924887

    check by using the yx key
    enter
    1÷15
    =
    yx
    2.309
    =

    you should get .001924887

    2.
    logx (4.44 * 10^4) = 4.44
    so x^4.44 = 4.44 *10^4
    log x^4.44 = log(4.44 * 10^4)
    4.44 logx = log 4.44 + log 10^4
    log x = 4.64738..
    x = 44400

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