ok this is tough...

Simplify: ln((2xy^3))/(sqaure root(z))

Question

ok this is tough...

Simplify: ln((2xy^3))/(sqaure root(z))

myininaya · Answer

do you mean expand?
$$\ln(\frac{2xy^3}{\sqrt{x}})=\ln(2xy^3)-\ln(\sqrt{x})=\ln(2)+\ln(x)+\ln(y^3)-\ln(x^\frac{1}{2})$$
$$=\ln(2)+\ln(x)+3\ln(y)-\frac{1}{2}\ln(x)$$

anonymous · Answer

is that what simplify means? all it says is simplify

myininaya · Answer

lol i don't know what simplify means 
let me get satellite

myininaya · Answer

oops that second x was suppose to be a z

anonymous · Answer

haha yeah i caught that

myininaya · Answer

$$\ln(\frac{2xy^3}{\sqrt{z}})=\ln(2xy^3)-\ln(\sqrt{z})=\ln(2)+\ln(x)+\ln(y^3)-\ln(z^\frac{1}{2})$$
$$=\ln(2)+\ln(x)+3\ln(y)-\frac{1}{2}\ln(z)$$

anonymous · Answer

Thank you so much!

myininaya · Answer

but hey i don't know what simplify means lol
so i told satellite to come here
so he can give his opinion

anonymous · Answer

ok gosh youre so helpful

anonymous · Answer

this one?

myininaya · Answer

yes we don't know what simplify means

anonymous · Answer

yes sir!

myininaya · Answer

and simplify is your favorite word
i just thought we we were to expand because thats the only i can see to do

anonymous · Answer

ok you did it.  this is not called "simplifying" however, but you have the right answer

anonymous · Answer

sometimes you are asked to write something as a single log
sometimes you are asked to write something as the sum and product of logs
this one is the second one

myininaya · Answer

i don't like the word simplify anymore

anonymous · Answer

there is absolutely nothing "simpler" about one form or the other.  depends on what your aim is
and frankly if your math teacher wrote "simplify" in this case, rather than saying what he or she wanted, they should not be teaching math

anonymous · Answer

haha thanks! thats my Texas A&M calc prof for ya there...

myininaya · Answer

lol

anonymous · Answer

ok can i ask you one more quick question?

myininaya · Answer

what is it

anonymous · Answer

evaluate: cos^-1 (-square root(3/2))

myininaya · Answer

$$\cos^{-1}(-\sqrt{\frac{3}{2}})   $$
that right?

anonymous · Answer

oh no thats all right except its negative sqaure root of 3 divided by 2

anonymous · Answer

i will bet it is 
$$\cos^{-1}(\frac{\sqrt{3}}{2})$$

myininaya · Answer

$$\cos^{-1}(\frac{-\sqrt{3}}{2})$$

anonymous · Answer

i forgot the minus sign.  sorry.  myininaya has it

anonymous · Answer

yes thats right! now evaluate?

anonymous · Answer

im supposed to get a degree or something

anonymous · Answer

ok you sure i dont need a radian or degree?

myininaya · Answer

lol ok so do you have your cheat sheet

myininaya · Answer

your unit circle

anonymous · Answer

yes i do

myininaya · Answer

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