## anonymous one year ago Find the inverse of y=log base2 (x-5)+2.

1. Nnesha

first step swap x and y $\huge\rm x =\log_2 (y-5)+2$ now try to solve for y

2. Nnesha

move the 2 to the left side and then convert log to exponential form

3. anonymous

I'm getting stuck after 2^log base2 (y-5) which is equal to y-5

4. Nnesha

i'm sorry what do you mean by 2^log ?

5. anonymous

so yes technically it looks like this x+2 = y-5 then x = y-3.

6. anonymous

2 to the power of log_2 (y-5) is equal to y - 5 after raising 2 to each side

7. Nnesha

well you have to move 2 to the left side so subtract 2 both sides $\huge\rm x =\log_2 (y-5)+2$ $\huge\rm x-2=\log_2(y-5)$ right ? now convert log to exponential form

8. Nnesha

the*

9. Nnesha

|dw:1439243974430:dw| that's how you should convert log to exponential form

10. Nnesha

let me know if you have any question

11. anonymous

I solved like this

12. anonymous

inverse: switch x and y, solve for y log(base2)(x-5)+2=y switch log(base2)(y-5)+2=x subtract 2 from each side log(base2)(y-5)=x-2 raise each side to two to get ride of the log 2^(y-5)=2^(x-2) simplify 2^y+0.03125=2^x+.25 subtract 0.03125 from each side 2^y=2^x+.28175 take log base two of each side to bring y down y=log(base 2)(2^x+.28175)

13. anonymous

But the thing is this solution is wrong

14. anonymous

Had this been correct it would had a inverse graph of the original equation.

15. Nnesha

good but i don't know ... why did you write 2^(y-5) ?? it should be $\huge\rm 2^{(x-2)}= y-5$

16. Nnesha

now add 5 both sides ....

17. anonymous

oh, that's what I was referring to in the start of this thread but still my solution is not coming up after applying that.

18. Nnesha

do you have options ?(answer choices ?

19. anonymous

I mean the graphs to check

20. anonymous

No, it is not MCQ. lol

21. Nnesha

oh okay gimme a sec i'll graph

22. Nnesha

23. Nnesha
24. anonymous

uhhh. my graphing cal. is not showing that. lol I was correct the whole time and here we are.

25. anonymous

Banged my head for 1 hr. on this stupidity lol

26. anonymous

Desmos, right ?

27. Nnesha

yes

28. Nnesha

wait gimme a sec i'll use Ti-84 ;P lol

29. anonymous

I prefer wolfram alpha although, there are some ranges which desmos fails to achieve. WA automatically adjusts the window according to the range. :-D

30. Nnesha

ugh hmm desmos is better than T-84... ;/

31. anonymous

yep but Wolfram Alpha senior to desmos as well :P

32. Nnesha

true

33. Nnesha

good luck! :=)

34. anonymous

Thanks. Have a nice day !

35. Nnesha

stupid typos -.-

36. anonymous

rofl !!!