## Megaforte8600 one year ago ln 2 - ln (3x + 2) = 1 Find X

1. mathmale

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

2. Megaforte8600

ln 2/ (3x + 2)

3. 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.

4. Megaforte8600

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

5. mathmale

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

6. Megaforte8600

no

7. Megaforte8600

i forgot how to

8. mathmale

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

9. mathmale

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

10. Megaforte8600

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

11. 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.

12. Megaforte8600

2/ (3x + 2) = e

13. 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.

14. Megaforte8600

im still confused

15. myininaya

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

16. myininaya

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

17. Megaforte8600

ok ^_^ thanks