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- anonymous

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

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- anonymous

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

- schrodinger

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- mathmale

An important rule of logarithms is this : ln a - ln b = ln (a/b).
Given that, what is ln 2 - ln (3x+2)?

- anonymous

ln 2/ (3x + 2)

- mathmale

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.

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- anonymous

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

- mathmale

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

- anonymous

no

- anonymous

i forgot how to

- mathmale

Use the fact that e^(ln a) = a.
If this is true (which it is), then what is \[e ^{\ln \frac{ 2 }{ 3x+2 }}?\]

- mathmale

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

- anonymous

ok, so its now
(2/3x + 2) = 1

- mathmale

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.

- anonymous

2/ (3x + 2) = e

- mathmale

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.

- anonymous

im still confused

- myininaya

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

- myininaya

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

- anonymous

ok ^_^ thanks

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