anonymous
  • anonymous
if log w= (1/5)log x - log y, then w =
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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zepdrix
  • zepdrix
A log rule: \(\large\rm \color{orangered}{b\cdot\log(a)=\log(a^b)}\) Apply this first to the log x term.
anonymous
  • anonymous
log x^1/5 -log y??
zepdrix
  • zepdrix
Good :)

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zepdrix
  • zepdrix
Another log rule: \(\large\rm \color{royalblue}{\log(a)-\log(b)=\log\left(\frac{a}{b}\right)}\)
anonymous
  • anonymous
so logw= (log x^1/5)/(log y)
anonymous
  • anonymous
in other terms: log w = x^1/5/y ??
zepdrix
  • zepdrix
woops! :O \(\large\rm \color{blue}{\log(a)-log(b)\ne \frac{\log(a)}{\log(b)}}\)
zepdrix
  • zepdrix
\[\large\rm \log(x^{1/5})-\log(y)=\log\left(\frac{x^{1/5}}{y}\right)\]The rule gives us a `single log`, ya?
zepdrix
  • zepdrix
So then,\[\large\rm \log (w)=\log\left(\frac{x^{1/5}}{y}\right)\]
anonymous
  • anonymous
so the answer is : log w = log (x^1/5/y)
zepdrix
  • zepdrix
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,\[\large\rm \implies\quad a=b\]
anonymous
  • anonymous
how can i make the bases the same?
zepdrix
  • zepdrix
They are the same already! :) When the base is not labeled, then it is by default a base of 10. So we have:\[\large\rm \log_{10}(w)=\log_{10}\left(\frac{x^{1/5}}{y}\right)\]
anonymous
  • anonymous
oh okay. so the log w is equal to x^1/5 divided by y
zepdrix
  • zepdrix
not the log of w, just the w! :) The insides are equal.\[\large\rm \log_{10}(\color{orangered}{w})=\log_{10}\left(\color{orangered}{\frac{x^{1/5}}{y}}\right)\qquad\implies\qquad \color{orangered}{w}=\color{orangered}{\frac{x^{1/5}}{y}}\]
anonymous
  • anonymous
I get it now. Since they are asking for w i just give them the value that w is equal to
zepdrix
  • zepdrix
yes. yay team, we did it \c:/
anonymous
  • anonymous
Thank you very much :) I appreciate you help

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