## anonymous one year ago Solve the equation log x = 2 log (mx) for x in terms of m.

1. 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:$\large\rm \color{\orangered}{b\cdot \log(a)=\log(a^b)}$

2. zepdrix

Make sure you apply the 2 to BOTH the m and the x.

3. 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!$\large\rm stuff=other~stuff$

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

Ya, lots of fun ways to approach logs :)

6. 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 $1 = 2 \log_x mx$ $x^{\frac{1}{2}} = mx$