Find the inverse of y=log base2 (x-5)+2.

- anonymous

Find the inverse of y=log base2 (x-5)+2.

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- Nnesha

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

- Nnesha

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

- anonymous

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

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## More answers

- Nnesha

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

- anonymous

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

- anonymous

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

- 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

- Nnesha

the*

- Nnesha

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

- Nnesha

let me know if you have any question

- anonymous

I solved like this

- 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)

- anonymous

But the thing is this solution is wrong

- anonymous

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

- Nnesha

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

- Nnesha

now add 5 both sides ....

- 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.

- Nnesha

do you have options ?(answer choices ?

- anonymous

I mean the graphs to check

- anonymous

No, it is not MCQ. lol

- Nnesha

oh okay gimme a sec i'll graph

- Nnesha

okay just asking ;P

- Nnesha

http://prntscr.com/835itz

- anonymous

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

- anonymous

Banged my head for 1 hr. on this stupidity lol

- anonymous

Desmos, right ?

- Nnesha

yes

- Nnesha

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

- 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

- Nnesha

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

- anonymous

yep but Wolfram Alpha senior to desmos as well :P

- Nnesha

true

- Nnesha

good luck! :=)

- anonymous

Thanks. Have a nice day !

- Nnesha

stupid typos -.-

- anonymous

rofl !!!

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