Question

Logarithim Problem

Answer 1

Gimme a sec

Answer 2

\[\ln (x + 2) - \ln x = \ln (x + 5)\]

Answer 3

Just asking to solve.

Answer 4

log rule 2, combine the ln(x+2) and the ln(x) on the left into one ln

Answer 5

\[\ln \frac{ x + 2 }{ x } = \ln (x + 5)\]

Answer 6

good, now when you raise both sides to the power of e you just get

(x+2)/x = x + 5

then it's just algebra to solve for x

Answer 7

let me know what you get

Answer 8

Sorry. Got pulled away.

\[\frac{ x + 2 }{ x } = x + 5\]

\[x + 2 = x^2 + 5x\]

\[x^2 + 4x - 2 = 0\]

Quadratic Formula

\[\frac{ -4 \pm \sqrt (4^2 -4(1)(-2) }{ 2(1) }\]

\[\frac{ -4 \pm \sqrt24 }{ 2 } \]

\[\frac{ -4 \pm 2 \sqrt 6 }{ 2 }\]

\[-2 \pm \sqrt 6\]

Answer 9

good, that's what I end up getting too

Answer 10

I believe you also have to check for extraneous solutions though

Answer 11

so you would plug in -2 + root(6) and -2 - root(6) into both equations to make sure both ln terms are defined

Answer 12

Oh yeah

Answer 13

Only the positive one works for me.

Answer 14

yup that's what I got too, gj

Answer 15

If I may ask, how did you check for extraneous solutions.

Answer 16

we have an ln(x) term so x must be positive

Answer 17

that automatically eliminates the -2 - root(6) solution

then I just plugged in -2 + root(6) into the original equation and the math worked out fine

Answer 18

The polynomial or the first ln equation

Answer 19

both should work

Answer 20

ln(-2 + sqrt(6) + 2) - ln(-2+sqrt(6)) = ln(-2 + sqrt(6) + 5))

if you are using a calculator be careful with parentheses

Answer 21

both sides are ~1.695521979

Answer 22

Yeah, I was getting something returned weird, and alas, it was a parentheses. Thank you :)