I lost a step?? how did he go from step 10 to 11 ?????

[real_name_x]

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

2. e^(2x) = 2 + (1/(x+2))

3. 2x(ln(e)) = ln[2 + (1/(x+2))]

4. 2x = ln [2+(1/(x+2))] * Remember, ln(e) = 1

5. 2x = ln [2(x+2)/(x+2) + 1/(x+2)]

6. 2x = ln [(2x+5)/(x+2)]

7. e^(2x) = (2x+5)/(x+2)

8. e^(2x) * (x+2)= (2x+5)

9. e^(2x) * (x+2) - 2x = 5

10. e^2 * e^x * (x+2) - 2x = 5 *
*
11. e^2 * x * (x+2) - 2x = 5 *

12. e^2 * (x^2+2x) - 2x = 5

how did you get rid of the e^x and make it just x ????

 

[stapel]

Wouldn't it be better if you asked whoever provided you with this solution, why he did what he did...? :shock:

Note: I don't believe this equation can be solved (I'm guessing that's what you're supposed to do with it), at least not algebraically. Sorry.

Eliz.

 

[skeeter]

got news for you, Zeke ... your original equation cannot be solved for x algebraically.

you sure it's \(\displaystyle \L e^{2x} - \frac{1}{x+2} = 2\) ?

 

[Deleted member 4993]

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

2. e^(2x) = 2 + (1/(x+2))

3. 2x(ln(e)) = ln[2 + (1/(x+2))]

4. 2x = ln [2+(1/(x+2))] * Remember, ln(e) = 1

5. 2x = ln [2(x+2)/(x+2) + 1/(x+2)]

6. 2x = ln [(2x+5)/(x+2)]

7. e^(2x) = (2x+5)/(x+2)

8. e^(2x) * (x+2)= (2x+5)

9. e^(2x) * (x+2) - 2x = 5

10. e^2 * e^x * (x+2) - 2x = 5 * Incorrect e^(2x) is NOT equal to e^2 * e^x
*
11. e^2 * x * (x+2) - 2x = 5 *

12. e^2 * (x^2+2x) - 2x = 5

how did you get rid of the e^x and make it just x ????