Question

I need help to simplify this equation

Answer 1

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

Answer 2

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

secod step is this
\[\ln (1) - 1/2\ln (x) - \ln(x) + 3\ln(x)\]

Answer 3

\[\ln (1) = 0\]

so we have, \[-1/2\ln(x) - \ln(x)-3\ln(x)\]

Answer 4

what is the next step

Answer 5

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

Answer 6

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 \(\ln(x)\)

Answer 7

\[\frac{ 3lnx }{ 2 }\]

Answer 8

nice trick to substitute, much easier to see!

Answer 9

thanks alot!

Answer 10

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. :)