## anonymous one year ago Find the solution to the equation. e^5x=25

1. anonymous

is e an variable in your equation?

2. Nnesha

take ln both sides and (5x) is an exponent right ?

3. anonymous

yess

4. Nnesha

alright so you can take natural log both sides to cancel out e $\huge\rm \cancel {ln e}^x = x$

5. anonymous

ln25=5x?

6. Nnesha

$\huge\rm \color{ReD}{ln }e ^{5x} = \color{Red}{\ln} 25$

7. Nnesha

yes right

8. anonymous

okay so now what?

9. Nnesha

use calculator for ln 25

10. Nnesha

and then solve for x

11. anonymous

i got 3.2188 when i did ln25

12. Nnesha

okay so 5x = 3.2188 solve for x divide both sides by 5

13. anonymous

0.6437?

14. Nnesha

yes right

15. anonymous

could you help me with one more?

16. Nnesha

i'll try

17. anonymous

2e^x-1=0

18. Nnesha

so exponent is (x-1) or just x ?

19. anonymous

just x

20. Nnesha

$\huge\rm 2e^x -1 = 0$ first solve for e^x

21. anonymous

2e^x=1?

22. Nnesha

yes right now divide both sides by 2

23. anonymous

e^x=2?

24. Nnesha

no. what about one ?

25. Nnesha

2/1 = 2 but 1/2 isn't equal to 2

26. anonymous

0.5?

27. Nnesha

yes right right

28. Nnesha

e^x = .5 solve for x

29. anonymous

it would be .5, wouldnt it?

30. Nnesha

no how would you cancel out e ?

31. anonymous

ln.5=x

32. Nnesha

yes right ln.5 not just .5 :=)

33. anonymous

-0.6931

34. anonymous

okay this is the last one i promise! -3e^4x +11=2

35. Nnesha

right

36. Nnesha

same like the last one try it and let me know what you get i'll check it

37. anonymous

0.2747?

38. Nnesha

nice yes that's right :=)

39. anonymous

thank you! I get it now, but i just ran across this one that i dont know how to do it with the exponent like that , its e^x+1 =1.461

40. anonymous

i got 0.3791 so far but im stuck on dividing it by x+1

41. Nnesha

x is an exponent or x+1 is an exponent ?

42. anonymous

x+1

43. anonymous

is the answer -6.209?

44. Nnesha

alright you don't have to divide by x+1 remember to cancel out something thing from one side you have to apply opposite of addition/subtraction/division/multiplication so x+1 <--- here is x plus 1 adding so do opposite of one addition to cancel out one from left side

45. Nnesha

yes that's right! :-)