Question

ln(x)+ln(x-1)=1

so far ive completed the square and now have:
(x-1/2)^2=e+1/4

Answer 1

what happened?

Answer 2

what i think im supposed to do isnt what the book is showing i would square both sides next and get
x-1/2=sqrt(e+1/4)
then add the 1/2
x=1/2+sqrt(e+1/4)

Answer 3

start by applying product law

Answer 4

apply product rule on ln x + ln (x-1) what do you get?

Answer 5

ln(x(x-1))

Answer 6

good so..

\[\ln [x(x+1)] = 1\]
now... i can change 1 into ln (0)

agree?

Answer 7

uhh nevermind

Answer 8

change to exponential form

Answer 9

so e^1

Answer 10

he's already done all that.

Answer 11

right

x(x+1) = e

Answer 12

really?

Answer 13

yes but continue

Answer 14

my bad

Answer 15

x(x-1) = e
anyway

Answer 16

i dont mind lets do this step by step

Answer 17

distribute x into x-1

Answer 18

x^2-x=e

Answer 19

you're done... take the root of both sides and simplify...

Answer 20

now use completing the square method to get the third term in x^2 - x

Answer 21

(x-1/2)^2=e+1/4

Answer 22

now take the square root of both sides

Answer 23

x-1/2=sqrt(e+1/4)

Answer 24

wrong,..

\[x - \frac 12 = \pm \sqrt{e+\frac 14}\]
that plus-minus is important

Answer 25

lol correct my bad

Answer 26

so now add 1/2

Answer 27

andddd i think i see where i went wrong lol

Answer 28

the plus-minus?

Answer 29

x=1/2+_ sqrt(e+1/4)

Answer 30

that's not yet simplified though

Answer 31

express e + 1/4 as one fraction

Answer 32

(4e+1)/4?

Answer 33

right

Answer 34

now... simplify \[\sqrt{\frac{4e+1}4}\]

Answer 35

\[x=\frac{ 1 }{ 2 }\pm \sqrt{\frac{ 4e+1 }{ 4 }}\]

Answer 36

do you now the square root of 4?

Answer 37

x=1/2+-(sqrt (4e+1))/2

Answer 38

right. now express as one fraction

Answer 39

\[\frac{ 1 }{ 2 }(1\pm \sqrt{4e+1})\]

Answer 40

right. and that is how mathematicians solve problems. with meticulousnessand OCD

Answer 41

lol ive been on that problem for like 20 min thanks

Answer 42

just doing my part in helping an awesome user in beating satellite73's SmartScore