Express (1/2) Log x - 2 Log x =y as a single Log

[pianoplaya16]

(1/2) Log x - 2 Log x =y

How do I simplify this to a single Log?

I got Log .25 = y but I don't think it is correct. Can someone help me please. Thank you.

 

[pka]

\(\displaystyle \L y = \log \left( {\frac{{\sqrt x }}{{x^2 }}} \right)\)

 

[soroban]

Hello, pianoplaya16!

Simplify to a single log: \(\displaystyle \:\frac{1}{2}\cdot\log(x)\,-\,2\cdot\log(x)\)

You're expected to know the properties of logs.

\(\displaystyle \frac{1}{2}\cdot\log(x)\,-\,2\cdot\log(x)\;=\;\log\left(x^{\frac{1}{2}}\right)\,-\,\log\left(x^2\right) \;=\;\log\left(\frac{x^{\frac{1}{2}}}{x^2}\right)\)

. . \(\displaystyle =\:\log\left(x^{-\frac{3}{2}}\right)\;=\;-\frac{3}{2}\cdot\log(x)\)