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anonymous

  • one year ago

Solve the equation log x = 2 log (mx) for x in terms of m.

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  1. zepdrix
    • one year ago
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    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:\[\large\rm \color{\orangered}{b\cdot \log(a)=\log(a^b)}\]

  2. zepdrix
    • one year ago
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    Make sure you apply the 2 to BOTH the m and the x.

  3. zepdrix
    • one year ago
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    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!\[\large\rm stuff=other~stuff\]

  4. BAdhi
    • one year ago
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    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

  5. zepdrix
    • one year ago
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    Ya, lots of fun ways to approach logs :)

  6. IrishBoy123
    • one year ago
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    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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