## anonymous one year ago log(3x+5)-log(x-5)=log(8)

1. anonymous

i got it so log(3x+5/x-5)=log8 and dont know where to go from there

2. Nnesha

hint: $\huge\rm log_b x = \log_b y$ $\huge\rm\cancel { log_b} x = \cancel{\log_b} y$ x=y

3. anonymous

so 3x-5/x-5=8

4. Nnesha

yep now simple algebra

5. anonymous

i got -20 but the answer is 9

6. Nnesha

how did you get -20?

7. anonymous

i cross multiplied

8. anonymous

so 8x-40=3x+5

9. Nnesha

solve for x

10. anonymous

i got -20

11. Nnesha

show ur work

12. anonymous

oh i found my mistake thank you!

13. Nnesha

r u sure ? u got it ?

14. anonymous

yep! can i ask you one more though?

15. Nnesha

alright

16. anonymous

log8+3logx=3 which i know is log8+logx^3=3 but what do you do if theres no log on the other side?

17. Nnesha

apply log properties which one you should apply ?

18. anonymous

change of base?

19. Nnesha

yeah or convert log to exponential form just like we did before

20. Nnesha

nope there is a variable so you can't use change of base formula

21. anonymous

how would you do that though because isnt it 8x^3=3

22. Nnesha

log (8x^3) = 3

23. Nnesha

$\log = \log_{10}$

24. anonymous

but idk how you would make that exponential

25. Nnesha

|dw:1432768266869:dw|

26. anonymous

but theres no base

27. Nnesha

there is i just posted that

28. Nnesha

$\log = \log_{10}$

29. anonymous

oh ok so then i get 10 though and the answe r is 5

30. Nnesha

xo x = 5 ?

31. anonymous

10^3=x^3 which is 10

32. anonymous

oh i forgot the 8

33. anonymous

oh ok so x=5 got it thanks

34. Nnesha

yep

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