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Thread: Remove the logs

  1. #1
    Sep 2009

    Remove the logs

    Could someone help me out with answering these questions:

    Remove the logs:
    1. logT = -0.0051 log t + 1.7705
    2. log T = 0.0046 log t + 1.7202

    It's pretty urgent, so any help would be appreciated.

    T = temperature
    t = time
    They're both subbed in values only relevant to my assignment, so they have no value.
    Last edited by thecite; Sep 7th 2009 at 06:10 AM.
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  2. #2
    Super Member Aryth's Avatar
    Feb 2007
    Let's look at the first one...

    Recall the logarithm properties:

    Alog(B) = $\displaystyle \log{(B^A)}$
    log(A) - log(B) = log(A/B)

    So, we have:

    $\displaystyle \log{(T)} = -0.0051\log{(t)} + 1.7705$

    Using the first property:

    $\displaystyle \log{(T)} = \log{(t^{-0.0051})} + 1.7705$

    Now, we move all of the logarithms to the same side:

    $\displaystyle \log{(T)} - \log{(t^{-0.0051})} = 1.7705$

    Now, we use the second property:

    $\displaystyle \log{\left(\frac{T}{t^{-0.0051}}\right)} = 1.7705$

    $\displaystyle \log{(Tt^{0.0051})} = 1.7705$

    Can you finish from here?

    The second problem is done similarly.
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