ln (cubed root((x^2)y))/(z^4) Use the power, quotient, and product properties of logarithms to write this as an equivalent expression
ln (cubed root((x^2)y))/(z^4) Use the power, quotient, and product properties of logarithms to write this as an equivalent expression
How about you do it yourself like you're supposed to ?
I honestly cannot figure it out.
The three relevant properties are:
log(x^n) = n*log(x)
log(xy) = log(x) + log(y)
log(x/y) = log(x) - log(y)
So here, we have
ln(cube root((x^2)y)/(z^4))
(1/3)*ln(((x^2)y)/(z^4)) [exponent rule, remembering that cube root(x) = x^(1/3)]
(1/3)*(ln((x^2)y) - ln(z^4)) [quotient rule]
(1/3)*(ln(x^2)+ln(y)-ln(z^4)) [product rule]
(1/3)*(2*ln(x)+ln(y)-4*ln(z)) [exponent rule]
(2/3)ln(x) + (1/3)ln(y) - (4/3)ln(z) [simplify]
ITT "do my homework for me".
...Made it through 9 years of wow...
Cranica has the relevant properties. There's an error in her work though, since only the (x^2)y is inside the cube root, assuming the problem is correctly parenthesized in the first post. I would recommend against anyone else providing the complete answer - after all, we can't help Tetriss when the test comes.
To get you started though, note that the original problem is the log of a quotient, and so that's a good place to start splitting it apart.
Yeah, dealing with nested parentheses in plain text is a pain... I suspect the OP might be improperly parenthesized actually, since as-written the z^4 is outside the ln.
Why should we do your homework for you? You should do it yourself, if not you are fucked at the test.
Do what I did in high school man, get a smart girlfriend, keep her happy and let her do your homework for you. When she's done ask her to make you a sandwich in order to hard wire proper husband/wife mechanics in her brain. I mean just look at me now! I'm a manager at McDonald's and I'm probably gonna die of a heart attack by 40 with a half empty bottle of JD in my hand.
Learning, lol.
The answer to any question is always 2*.
*for a relative value of two in an undefined base system.
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try yahoo answers ... but honestly, the wiki page helps a lot or just google logarithm problems and try to figure it out on your own - think of it this way: if you find out how to do it yourself it's the best way to learn how to do it on the exam - read about the rules, look at a few example problems but apply the rules yourself !
good luck
The answer is open the math book and learn how to do it. If that still doesn't help, drop out of school and leach off the welfare system which my taxes provide you with.
I actually just did the problem since I was bored. Not gonna post it though