## anonymous one year ago I need help to simplify this equation

1. anonymous

$\ln (\frac{ 1 }{ \sqrt{x} }) - \ln (x) + \ln (x^3)$

2. anonymous

first step is this: $\ln (1) - \ln (x ^{1/2}) - \ln (x) + \ln (x^3)$ secod step is this $\ln (1) - 1/2\ln (x) - \ln(x) + 3\ln(x)$

3. anonymous

$\ln (1) = 0$ so we have, $-1/2\ln(x) - \ln(x)-3\ln(x)$

4. anonymous

what is the next step

5. mathslover

Simply take $$\ln(x)$$ common ..

6. mathslover

For a second, let us imagine $$\ln(x)$$ as any variable $$t$$ So, we have: $$-\cfrac{1}{2}t -t - 3t$$ Now, you know how to simplify this, don't you? After simplifying, put $$t$$ back as $$\ln(x)$$

7. anonymous

$\frac{ 3lnx }{ 2 }$

8. anonymous

nice trick to substitute, much easier to see!

9. anonymous

thanks alot!

10. mathslover

Uhm... I guess, you need to check your arithmetic again. We have : $$\cfrac{-1}{2} t - t - 3t = -t\left( \cfrac{1}{2} + 1 + 3 \right) = -t \left( \cfrac{9}{2} \right) = \cfrac{-9t}{2}$$ Or : $$-\cfrac{9}{2} \ln x$$ And you're welcome. :)