Use the properties of logarithms to write the following expression as a sum or difference of simple logarithmic term.

In(x4square root y)

Question

Use the properties of logarithms to write the following expression as a sum or difference of simple logarithmic term. 

In(x4square root y)

callisto · Answer

Do you mean $$\ln x^4\sqrt{y}$$  for your question?

anonymous · Answer

no
4v

anonymous · Answer

v4

callisto · Answer

$$\ln x \sqrt[4]{y}$$ ?

anonymous · Answer

yes

callisto · Answer

$$\ln x \sqrt[4]{y}$$$$=\ln x + \ln\sqrt[4]{y}$$$$=\ln x + \ln y^{1/4}$$$$=\ln x + (1/4)\ln y $$

anonymous · Answer

Thank you

callisto · Answer

Welcome, but do you understand how to do it (or why I did it like that) ?

anonymous · Answer

I always get confused of with those question the logs and lns? do u have any helpful points to help me with?

callisto · Answer

Some, perhaps
$$\log x^n =nlogx$$
$$\log xy =logx + logy$$

callisto · Answer

Those are for your question only
and also you might find this helpful too
$$log(a/b) = loga -logb$$

anonymous · Answer

are lns the same BUT the diffrent is ln=e and log=10 right??

callisto · Answer

Plus one more point
$$\sqrt[n]{x} = x ^{(1/n)}$$So, $$\log \sqrt[n]{x} = \log x ^{(1/n)}= (1/n)\log x $$

callisto · Answer

Hmm.. these are the properties of logarithm, no matter what base it is , you can still apply it

ln is natural log with base e, while log is the common log, with base 10
which means lne =1, while log10 =1

callisto · Answer

Hmm, does that make it better or worse?

anonymous · Answer

of course, thank you also, now i understand this part, but when should I use the e and ln + 10 and log when the question says what?

callisto · Answer

I think it depends on the situation. If you are like given e in the question, probably using ln is more convenient, or else just use the common log. Plus, sometimes the question itself may give you the log with other bases, like 2, and so on. So use the one you think it is the most convenient :)

anonymous · Answer

that what I hate about math... lol :) thank you. i got sick of the complex stuff ugh. thank u very much again

callisto · Answer

(You're welcome) x2 . Math could be fun with more practice :)

anonymous · Answer

that is as like as our recent philosophy of life.

anonymous · Answer

thank u

callisto · Answer

You're welcome again :)

anonymous · Answer

Also, how to answer this

ln (8x-4)=ln2+lnx