anonymous
  • anonymous
Solve the equation log x = 2 log (mx) for x in terms of m.
Mathematics
schrodinger
  • schrodinger
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zepdrix
  • zepdrix
Hey there :) You can apply some rules of logs to get this one moving along. We can deal with the 2 by using this log rule:\[\large\rm \color{\orangered}{b\cdot \log(a)=\log(a^b)}\]
zepdrix
  • zepdrix
Make sure you apply the 2 to BOTH the m and the x.
zepdrix
  • zepdrix
Then you'll have something of this form: \(\large\rm \log(\text{stuff})=\log(\text{other stuff})\) And since the log function is one-to-one, we can determine that the insides must be equal!\[\large\rm stuff=other~stuff\]

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BAdhi
  • BAdhi
another way to do this is, expand the log on the right hand side \(\log(mx) = \log(m) + \log(x)\) then solve for \(\log(x)\) and find x later
zepdrix
  • zepdrix
Ya, lots of fun ways to approach logs :)
IrishBoy123
  • IrishBoy123
and none dumber than this :-) \[\log x = 2 \log (mx)\] \[\frac{\log_x x}{log_x b} = 2 \frac{\log_x mx}{log_x b}\] where b is what you started in \[1 = 2 \log_x mx\] \[x^{\frac{1}{2}} = mx \]

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