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anonymous

  • one year ago

if log w= (1/5)log x - log y, then w =

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  1. zepdrix
    • one year ago
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    A log rule: \(\large\rm \color{orangered}{b\cdot\log(a)=\log(a^b)}\) Apply this first to the log x term.

  2. anonymous
    • one year ago
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    log x^1/5 -log y??

  3. zepdrix
    • one year ago
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    Good :)

  4. zepdrix
    • one year ago
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    Another log rule: \(\large\rm \color{royalblue}{\log(a)-\log(b)=\log\left(\frac{a}{b}\right)}\)

  5. anonymous
    • one year ago
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    so logw= (log x^1/5)/(log y)

  6. anonymous
    • one year ago
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    in other terms: log w = x^1/5/y ??

  7. zepdrix
    • one year ago
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    woops! :O \(\large\rm \color{blue}{\log(a)-log(b)\ne \frac{\log(a)}{\log(b)}}\)

  8. zepdrix
    • one year ago
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    \[\large\rm \log(x^{1/5})-\log(y)=\log\left(\frac{x^{1/5}}{y}\right)\]The rule gives us a `single log`, ya?

  9. zepdrix
    • one year ago
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    So then,\[\large\rm \log (w)=\log\left(\frac{x^{1/5}}{y}\right)\]

  10. anonymous
    • one year ago
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    so the answer is : log w = log (x^1/5/y)

  11. zepdrix
    • one year ago
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    Well they want w, not log(w). So we still have a little ways to go :) When the logs are the same base, as in this example, \[\large\rm \log(a)=\log(b)\]Then it means the contents of the logs are equal,\[\large\rm \implies\quad a=b\]

  12. anonymous
    • one year ago
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    how can i make the bases the same?

  13. zepdrix
    • one year ago
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    They are the same already! :) When the base is not labeled, then it is by default a base of 10. So we have:\[\large\rm \log_{10}(w)=\log_{10}\left(\frac{x^{1/5}}{y}\right)\]

  14. anonymous
    • one year ago
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    oh okay. so the log w is equal to x^1/5 divided by y

  15. zepdrix
    • one year ago
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    not the log of w, just the w! :) The insides are equal.\[\large\rm \log_{10}(\color{orangered}{w})=\log_{10}\left(\color{orangered}{\frac{x^{1/5}}{y}}\right)\qquad\implies\qquad \color{orangered}{w}=\color{orangered}{\frac{x^{1/5}}{y}}\]

  16. anonymous
    • one year ago
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    I get it now. Since they are asking for w i just give them the value that w is equal to

  17. zepdrix
    • one year ago
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    yes. yay team, we did it \c:/

  18. anonymous
    • one year ago
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    Thank you very much :) I appreciate you help

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