Question

Can someone show me how to expand log (x^3sqrt(x^2+1))/(y^2(x+1)^4)

Answer 1

log (x^3sqrt(x^2+1))/(y^2(x+1)^4)
do you think the solution is like this?
(x^3sqrt(x^2+1)
=log ---------------------- ..........................yes or no?
(y^2(x+1)^4))
=log (x^3sqrt(x^2+1) - log (y^2(x+1)^4)) ................yes or no?
=log (x^3) + log(x^2+1)^1/2 - [ log (y^2) + log(x+1)^4))] ...... yes or no?
=3log (x) +(1/2) log(x^2+1) - [2 log (y) + 4log(x+1)].......... yes or no?
=3log (x) +(1/2) log(x^2+1) - 2 log (y) - 4log(x+1)..............final answer,,,,.yes or no?

Answer 2

I honestly don't know how to even do it.. the equation looks like this:
\[Expand:\log\frac{ x^3\sqrt{x^2+1} }{ y^2(x+1)^4 }\]

Answer 3

yup the problem i copied is correct based on what you wrote now

Answer 4

okay. so the final answer looks like this? : \[3\log(x)+\frac{ 1 }{ 2 }\log(x^2+1)-2\log(y)-4\log(x+1)\]

Answer 5

yes you are correct.... :D

Answer 6

Thanks so much! Do you by any chance know how to write a ln equation into a single ln?
ie : 2ln(x+1)-ln(x+2)-3lnx

Answer 7

ypu do the same process backward its the same thing

Answer 8

2ln(x+1)-ln(x+2)-3lnx check if the solution is correct
=ln(x+1)^2 - ln(x+2)-lnx^3 separate all the negative signs to the right
=ln(x+1)^2 -( ln(x+2)+lnx^3) ....... yes or no?

l(x+1)^2
= ln ------------- ...................... yes or no?
(x+2)(x^3)

Answer 9

why is there an l infront of (x+1)^2 for the final answer?

Answer 10

@mark_o.

Answer 11

ln means natural logarithm of base e
while log means log to the base 10

Answer 12

ohhhh. okay i get it thank you so much for your help!!

Answer 13

ok yw... have fun.... good luck now :D