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Math Help - Express in terms of natural logs...

  1. #1
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    Express in terms of natural logs...

    Express \log_{7}4 in terms of natural logarithms. Do not find a numerical answer.



    Thanks for your help.. I really appreciate it.
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  2. #2
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    Quote Originally Posted by Savior_Self View Post
    Express \log_{7}4 in terms of natural logarithms. Do not find a numerical answer.



    Thanks for your help.. I really appreciate it.
    If y= log_7(4) the 4= 7^y, from the definition of "log". Now solve for y by taking the natural logarithm of both sides.
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    Quote Originally Posted by Savior_Self View Post
    Express \log_{7}4 in terms of natural logarithms.
    Hint: Use the change-of-base formula.
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  4. #4
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    alright, I believe I've got it.


    x = \log_{7}4

    7^x = 4

    ln 7^x = ln 4

    x  ln 7 = ln 4

    x = \frac{ln4}{ln7}


    all good?
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  5. #5
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    Quote Originally Posted by Savior_Self View Post
    alright, I believe I've got it.


    x = \log_{7}4

    7^x = 4

    ln 7^x = ln 4

    x ln 7 = ln 4

    x = \frac{ln4}{ln7}


    all good?
    All good!!
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  6. #6
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    Quote Originally Posted by Savior_Self View Post
    alright, I believe I've got it.


    x = \log_{7}4

    7^x = 4

    ln 7^x = ln 4

    x  ln 7 = ln 4

    x = \frac{ln4}{ln7}


    all good?
    Yes, but there is no point in doing all that. With the change of base formula (as stapel pointed out) you can change between log easy. Change of base says:

    \log_x y = \frac{\log_z x}{\log_z y}

    It's pretty easy to use.
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  7. #7
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    Quote Originally Posted by Korupt View Post
    Yes, but there is no point in doing all that. With the change of base formula (as stapel pointed out) you can change between log easy. Change of base says:

    \log_x y = \frac{\log_z x}{\log_z y}

    It's pretty easy to use.
    Nay, your answer is a factor of -1 out.

    log_x y = -\frac{log_z x}{log_z y} = \frac{log_z y}{log_z x}
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