Question

ln 2 - ln (3x + 2) = 1

Find X

Answer 1

An important rule of logarithms is this : ln a - ln b = ln (a/b).

Given that, what is ln 2 - ln (3x+2)?

Answer 2

ln 2/ (3x + 2)

Answer 3

good. Now, \[\ln \frac{ 2 }{ 3x+2 }=1.\] how would you now get rid of the ln operator? We want to solve this equation for x.

Answer 4

e^ln ( 2/ 3x + 2 ) = e^1

Answer 5

Hey, that's really cool. Can you now simplify this equation?

Answer 6

no

Answer 7

i forgot how to

Answer 8

Use the fact that e^(ln a) = a.

If this is true (which it is), then what is \[e ^{\ln \frac{ 2 }{ 3x+2 }}?\]

Answer 9

The right side is simply e^1, or e.

Answer 10

ok, so its now

(2/3x + 2) = 1

Answer 11

Other than that your 3x+1 should be within parentheses, yes! Mind re-writing that? Don't need parenthesis in front of the first 2.

Answer 12

2/ (3x + 2) = e

Answer 13

Yes, or \[\frac{ 3x+2 }{ 2 }=\frac{ 1 }{ e }\] One way of solving this would be to cross-multiply. We have to isolate x on the left side of the equation.
I need to log off now, but think you're well on the way to solving this problem properly. See you again soon, I hope.

Answer 14

im still confused

Answer 15

are you confused on the cross multiplication part?
he means if you have
\[\frac{a}{b}=\frac{c}{d} \text{ you can do } ad=cb\]

Answer 16

and remember we are solving for x
remember treat e like you would treat 2 or 3 or any other constant number

Answer 17

ok ^_^ thanks