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Math Help - Write As Single Log

  1. #1
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    Write As Single Log

    Use the properties of logs to rewrite each expression as a single log. (log_b K - log_b M)- log_b a

    MY WORK:

    (log_b K - log_b M)- log_b a

    Write as a single log.

    I applied the rule log_(M/N) = log_b M - log_b N twice.

    log_b(K/M) - log_b a....I could not stop here, right?

    log_b[(K - a)/(M - a)]

    Is this right? If not, why not?




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  2. #2
    A riddle wrapped in an enigma
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    Quote Originally Posted by magentarita View Post
    Use the properties of logs to rewrite each expression as a single log. (log_b K - log_b M)- log_b a

    MY WORK:

    (log_b K - log_b M)- log_b a

    Write as a single log.

    I applied the rule log_(M/N) = log_b M - log_b N twice.

    log_b(K/M) - log_b a....I could not stop here, right?

    log_b[(K - a)/(M - a)]

    Is this right? If not, why not?

    Here's what I did.

    \log_bK-\log_bM-\log_ba \Rightarrow \log_b\frac{K}{M}-\log_ba\Rightarrow\log_b\frac{\frac{K}{M}}{a}\Righ  tarrow\boxed{\log_b\frac{K}{Ma}}


    I checked it with K=100, M=1000, a=10000 and using common log base 10.


    \log_bK-\log_bM-\log_ba \Rightarrow\log_{10}100-\log_{10}1000-\log_{10}10000={\color{red}-5}


    \log_b\frac{K}{Ma}\Rightarrow\log_{10}\frac{100}{1  000\cdot 10000}={\color{red}-5}
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  3. #3
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    ok.........

    Quote Originally Posted by masters View Post
    Here's what I did.

    \log_bK-\log_bM-\log_ba \Rightarrow \log_b\frac{K}{M}-\log_ba\Rightarrow\log_b\frac{\frac{K}{M}}{a}\Righ  tarrow\boxed{\log_b\frac{K}{Ma}}


    I checked it with K=100, M=1000, a=10000 and using common log base 10.


    \log_bK-\log_bM-\log_ba \Rightarrow\log_{10}100-\log_{10}1000-\log_{10}10000={\color{red}-5}


    \log_b\frac{K}{Ma}\Rightarrow\log_{10}\frac{100}{1  000\cdot 10000}={\color{red}-5}
    Thank you for breaking it down just a bit more.
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