## donovan11 4 years ago Solve the logarithmic equation for . Please round the answer to four decimal places, if necessary. ln(x-4)+ln(x+5)=1

1. donovan11

Reason I'm confused is because unlike log, in ln the exponential form is e^y=x and I'm having trouble solving the rest

2. amistre64

ln(a) + ln(b) = ln(ab)

3. donovan11

That's x^2+x-20?

4. amistre64

yep. now, ln(0) = 1 because e^0 = 1

5. myininaya

and also any number to the 0 power except 0 is 1

6. amistre64

your equation is really: x^2 +x - 20 = 0

7. myininaya

wait!

8. amistre64

or (x-4) (x+5) = 0

9. myininaya

e^1=e

10. myininaya

we have (x-4)(x+5)=e

11. amistre64

lol..... maybe it does, and maybe it doesnt :)

12. beens

yes myininaya

13. myininaya

if we do it like amistre we would make the problem much easier but also kindof wrong

14. myininaya

and kindof wrong is just wrong

15. donovan11

now im confused >_<

16. amistre64

horseshoe and handgranades me friend :)

17. myininaya

so we have x^2-9x+20+e=0

18. myininaya

oops -e

19. donovan11

wouldnt it be -e?

20. myininaya

Yes i blame amistre

21. myininaya

lol

22. beens

bring over 1 to the left at the start...before changinglg form...

23. amistre64

...its my liver pills...blame the liver pills :)

24. donovan11

so whats the answer?

25. myininaya

use quadractic formula x=(9@sqrt(81-4(1)(20-e))/2 where @ means + or -, but make sure your answer is positive because you cannot do ln(negative)

26. beens

sorry...doesn't make a difference what I said

27. beens

Quadratic formula the way to go

28. donovan11

this is what i put on the formula -1+squareroot(1^2 -4(1)(20-e))))/2

29. myininaya

no

30. myininaya

a=1 n=-9 c=20-e correct?

31. beens

c=-20-e

32. myininaya

b=-9*

33. beens

b=1

34. donovan11

no b =1

35. myininaya

dont listen to me

36. myininaya

im doing two things at once sorry

37. donovan11

my calculator wont work

38. myininaya

(-1+sqrt(1-4(-20-e))/2=4.2925 and (-1-sqrt(1-4(-20-e))/2=-5.2925 but we can't use -5.2925 since it is negative and the natural log of a negative number doesnt exist

39. amistre64

x can be negative if it is not the only thing controling the value of the log. the thing is: x-4 needs to be greater than 0 and, x+5 needs to be greater than 0. x >4 serves both cases.

40. myininaya

correct!

41. myininaya

that negative number gives you another negative number when you plug it into x-4