anonymous
  • anonymous
Express the given quantity as a single logarithm. 1/5 ln(x + 2)^5 + 1/2 [ln x − ln(x^2 + 3x + 2)^2]
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
ghazi
  • ghazi
\[\frac{ 1 }{ 5 }\log(x+2)^5+\frac{ 1 }{ 2 }[{\ln x- \ln (x^2+3x+2)^2}]= \frac{ 1 }{ 5 }*5 \log(x+2)+\frac{ 1 }{2 }[\ln x- \ln(x^2+3x+2)^2]\] i am sorry to say, this can't be unified because ln and log have different bases
anonymous
  • anonymous
All of them are base e, surely?
ghazi
  • ghazi
oops my bad

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

anonymous
  • anonymous
Are there any nice identities for\[\log(a)^b\]? Maybe I'm being stupid.
anonymous
  • anonymous
Also- does anyone know how to have latex flow with your text rather than indent?
ghazi
  • ghazi
no you are right ...and it can be simplified
jhonyy9
  • jhonyy9
do you know the property of logarithm ? so like ln a + ln b = ? or ln a -ln b = ? or ln a^2 = ?
jhonyy9
  • jhonyy9
you dont like cooperating nothing ? i like help you here ... come on !!!
anonymous
  • anonymous
i'm confused
jhonyy9
  • jhonyy9
why ? so you know that ln a + ln b = ln a*b yes ?
anonymous
  • anonymous
yes
jhonyy9
  • jhonyy9
so than do you know how many will be ln a^2 =
jhonyy9
  • jhonyy9
or ln a - ln b =
anonymous
  • anonymous
ln(a/b)
jhonyy9
  • jhonyy9
yes and ln a^2 =
anonymous
  • anonymous
2ln a
jhonyy9
  • jhonyy9
yes right sure so than these property of logarithms can us in case of your exercise too ?
anonymous
  • anonymous
(ln(x + 2) (1/2 ln x / 2ln(x^2 + 3x + 2))
anonymous
  • anonymous
[ln(x + 2)] [1/2( ln x / 2ln(x^2 + 3x + 2))]
jhonyy9
  • jhonyy9
so the first part is right but the secondly you need to separate 1/5 ln(x+2)^5 = 5/5 ln(x+2) = ln(x+2) this is right so in the second part there are 1/2 (ln x - ln(x^2 +3x +2)^2) = 1/2 (ln (x/(x^2 +3x +2)^2) = ln (x/(x^2 +3x +2)^2)^(1/2) do you understand till now ? can you continue it ?
anonymous
  • anonymous
yess
jhonyy9
  • jhonyy9
so than how will be ?
anonymous
  • anonymous
[ln(x+2)] [ln (x/(x^2 +3x +2)^2)^(1/2)]
jhonyy9
  • jhonyy9
why ? than you know that (a^2)^(1/2) =a^(2/2) =a so than what will be ?
jhonyy9
  • jhonyy9
and you know that ln a +ln b = ln a*b
anonymous
  • anonymous
[ln(x+2)] [ln (x/(x^2 +3x +2)]
jhonyy9
  • jhonyy9
not is right please check it because there is just (x^2 +3x +2)^2 and x on numerator have not exponent 2 so what sign that not can be simplified by 1/2 OK ?
jhonyy9
  • jhonyy9
do you understand it sure ?
anonymous
  • anonymous
no
jhonyy9
  • jhonyy9
so the first part is right sure will be ln(x+2) OK . in the second part there are 1/2 (ln x - ln(x^2 +3x +2)^2) = 1/2 (ln (x/(x^2 +3x +2)^2)) = ln (x^(1/2) /((x^2 +3x +2)^2)^1/2 = ln (x^1/2) /(x^2 +3x +2) so can you continue it now ?
jhonyy9
  • jhonyy9
so than will result there ln (x+2) + ln (x^1/2) /(x^2 +3x +2) so from this can you continue it ?
jhonyy9
  • jhonyy9
are you here ?
jhonyy9
  • jhonyy9
so than will be using the property of logarithm log a +log b = log a*b so than will be ln ((x+2)*x^1/2 ) /(x^2 +3x +2)
jhonyy9
  • jhonyy9
so x^2 +3x +2 how can you factoriz it ?
jhonyy9
  • jhonyy9
do you know ?
jhonyy9
  • jhonyy9
so x^2 +3x +2 = (x+2)(x+1) is right ?
jhonyy9
  • jhonyy9
so than will be ln (x+2)x^(1/2) /(x+2)(x+1) so simplifie by (x+2) and will result ln x^1/2 /(x+1) so do you understand it now sure ?

Looking for something else?

Not the answer you are looking for? Search for more explanations.