Question

Express the given quantity as a single logarithm.
1/5(ln(x+2)^5)+1/2[ln(x) - ln(x^2+3x+2)^2]

Answer 1

\[\frac{ 1 }{ 5 } \ln (x+2)^5 +\frac{ 1 }{ 2 } \left[ \ln x - \ln (x^2 +3x+2)^2\right]\]

Answer 2

\[\frac{1}{5}\ln(x+2)^5=\ln(x+2)\] is a good start

Answer 3

before i combined i would actually distribute the \(\frac{1}{2}\) on the second set of parentheses
that would give
\[\frac{1}{2}\ln(x)-\ln(x^2+3x+2)\] as the two would cancel

Answer 4

ok so far?

Answer 5

Yep.

Answer 6

then
\[\frac{1}{2}\ln(x)=\ln(\sqrt{x})\] and then you are good to go

Answer 7

\[\ln(x+2)+\ln(\sqrt{x})-\ln(x^2+3x+2)\] combine as
\[\log(A)+\log(B)-\log(C)=\log(\frac{AB}{C})\]

Answer 8

oh and one more thing
since \(x^2+3x+2=(x+2)(x+1)\) you will be able to cancel a factor of \(x+2\) top and bottom

Answer 9

So the answer is \[\ln \frac{ \sqrt{x} }{ x+1 }\] ?

Answer 10

that is what i get, yes

Answer 11

seem reasonable?

Answer 12

Yes. It makes a lot more sense now. Thank you so much! :)

Answer 13

yw
now i have a question

Answer 14

is that really a chuck e cheese hat?

Answer 15

Yes. Yes, it is.

Answer 16

ho ho ho
nice

Answer 17

I didn't want to get a sunburn on my head, because that makes showering really terrible.
I'm not really a hat person, though, so I had to borrow one.

Answer 18

guess there was a 10 year old handy

Answer 19

There was a five-year old handy, yes. xD