ln(√2)+3ln2

Question

ln(√2)+3ln2

anonymous · Answer

The answer is (7/2) ln 2 but how do i get that?

nnesha · Answer

http://openstudy.com/study#/updates/54dae049e4b0ffc24cc3744f u look familiar

anonymous · Answer

I wanted to put it in the calculus 1 section, so i reposted, sorry

nnesha · Answer

hmm its okay :)

zale101 · Answer

When a constant is multiplied by ln of something, that would become the exponent. Correct? 
$3ln(2)$=$ln(2)^{3}$

anonymous · Answer

Yes @Zale101

zale101 · Answer

So $ 3ln(2)$=$ln(2)^3$=$ln(8)$

zale101 · Answer

When two natural logs are added together, what does that signifies?

anonymous · Answer

ln(a+b)

anonymous · Answer

wait no ln(ab)

zale101 · Answer

Yes.

zale101 · Answer

So, how would you write by using the product rule of logarithmic. 
$ln(\sqrt{2})+ln(8)$

anonymous · Answer

$$\ln8 \sqrt{2}$$

zale101 · Answer

Yes, now if you were to place that in a calculator. You'd get the same decimal answer for the transcendental number of (7/2) ln 2

anonymous · Answer

OHHHH I see. I thought the process of simplifying the equation automatically gave you 7/2, which was what i was confused about. 
I'm sorry but would you mind helping me with one more question? @Zale101

anonymous · Answer

I'm confused on what do when they give you 3. Such as $$2 \ln (1/3) - \ln 3 + \ln (1/9)$$ waht would I do here?

zale101 · Answer

$\Large 2^{7/2}$=$\Large 8\sqrt{2}$
Because
$8=2^{3}$
and $\sqrt{2}=2^{1/2}$
$\large 2^{3}*2^{1/2}$=$\large 2^{3+\frac{1}{2}}$=$\Large 2^{7/2}$

anonymous · Answer

Oh man, you're a genius. Thank you so much!!!  :DDDDDDDDD

nnesha · Answer

^^^^^^^^^^^true story

zale101 · Answer

$\color{red}2ln(1/3)−ln(3)+ln(1/9)$
$ln(1/3)^{\color{red}2}−ln(3)+ln(1/9)$
we see that two lns are subtracting each other, that means we use the log quotient rule
$[ln(1/3)^{\color{red}2}−ln(3)]+ln(1/9)$
$[ln(\large\frac{\frac{1}{9}}{3})]+ln(1/9)$
solve for $\Large \frac{1}{9}*\frac{1}{3}$, hence i flipped (reciprocal)of the denominator that was 3/1. 
That would equal $\Large\frac{1}{27}$
So, we would get $[\large ln(\large\frac{1}{27})]+ln(1/9)$
We are not done yet, because there's two ln's that are added together, so we would apply the product rule of logs.

zale101 · Answer

Refresh to get rid of the star thingies

zale101 · Answer

Anyways, to future solve future problem like these keep this image with you.

anonymous · Answer

Wow, You're always on here every time I need help haha. You also put so much effort into helping me understand this and I really really appreciate it. I think you explain things better than my own teacher does o.O 
Thank you so much @zale101 !!!

zale101 · Answer

No problem, i'm glad that i helped. Best wishes to you too!

zale101 · Answer

It's a coincidence, whenever I'm logged on here, I see your questions posted. I really appreciate your effort on trying to learn and to work on problems. I dont see many people do this. Good luck! :-)

anonymous · Answer

Thank you so much!!! :D @zale101

zale101 · Answer

No problem. Thanks for participating and welcome to OS!