PLZ help ASAP mathematicians?

Question

Write the following expression as a sum and/or difference of the logarithms.

log (all this next part is in one big parethesis: sqrt(x+2)/x^2-x


I know the rules....I just need the answer ASAP...I thought I knew the answer, but it was wrong and I don't know why? Please help me....I promise to give 10 to best answer! think the answer is (1/2 log (x+2)) - log x - log (x-2)........you all agree that just answered or anyone?

Answer 1

1/2 log(x+2) - log(x) - log(x-1)

Answer 2

Start with your equation:
log [ sqrt(x + 2) / (x² - x) ]

Sqrt is the same as raising to ½ power. And denominator is the same as raising to -1 power:
log [ (x + 2)^½ * (x² - x)^-1 ]

Use this rule: log (ab) = log(a) + log(b)
log [ (x + 2)^½ ] + log [ (x² - x)^-1 ]

Use this rule: log[x^k] = k log [x]:
½ log(x + 2) + (-1) log [ x² - x ]

Factor the second log:
½ log(x + 2) + (-1) log [ x(x - 1) ]

Use this rule: log (ab) = log(a) + log(b)
½ log(x + 2) + (-1) [ log (x) + log (x - 1) ]

Simplify:
½ log(x + 2) - log (x) - log (x - 1)

I think you have a slight typo in the last part of your answer...

P.S. Note: in step 1 you could have used the division rule too. log(a/b) = log(a) - log(b). That's essentially the same as what I did with the -1 power and the multiplication.

Answer 3

x^2 - x = x(x-1) so at the end should be log (x-1) not log (x-2). I agree with the rest though

Answer 4

y=sqrt(x+2)/(x^2-x)
sqrt(x+2)=(x+2)^(1/2)
(1/2)log(x+2) [ using x^a = a log (x)]
using log(a/b)=log(a)-log(b)
(1/2)log(x+2)-log(x^2-x)
=(1/2)log(x+2)-log(x(x-1))
=(1/2)log(x+2)-log(x)-log(x-1) is the answer.
You should have written (x^2-x) rather than x^2-x.

Answer 5

little or no. Her paintings change into better many times than not commentaries on previous fabric. The mainstream of mathematics isn't so in contact in conic sections from a really geometric perspective.

Answer 6

little or no. Her paintings change into better many times than not commentaries on previous fabric. The mainstream of mathematics isn't so in contact in conic sections from a really geometric perspective.