Inverse and Domain | Mathematics | Page 1

obsidian rain Apr 7, 2024, 10:00 PM

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g(x)=17(2)^0.15x

i know you do something with log but im so confused by everything

brisk impBOT Apr 7, 2024, 10:00 PM

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naive pecan Apr 7, 2024, 10:00 PM

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obsidian rain g(x)=17(2)^0.15x i know you do something with log but im so confused by everyth...

What are your confusions, sir?

obsidian rain Apr 7, 2024, 10:01 PM

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naive pecan What are your confusions, sir?

like i saw someone say that you have to put the log when you trying to find y and its the exponent or something but really now im confused on the whole process

naive pecan Apr 7, 2024, 10:01 PM

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Ok first step.

vernal phoenixBOT Apr 7, 2024, 10:02 PM

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𝔸dωn𝓲²s

naive pecan Apr 7, 2024, 10:02 PM

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They key to find the inverse is to solve for x here 🙂

obsidian rain Apr 7, 2024, 10:02 PM

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ye

naive pecan Apr 7, 2024, 10:02 PM

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So we can first divide by 17

vernal phoenixBOT Apr 7, 2024, 10:02 PM

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𝔸dωn𝓲²s

naive pecan Apr 7, 2024, 10:03 PM

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Now we use log, but the question is to which base?

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any ideas?

obsidian rain Apr 7, 2024, 10:03 PM

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this is where I have no idea lol idk the steps makes sense but then the log part I just don’t know tbh

naive pecan Apr 7, 2024, 10:04 PM

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ok relax.

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The base of the log is also the base of your exponential function

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what's the base of 2^0.15x?

obsidian rain Apr 7, 2024, 10:04 PM

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2

naive pecan Apr 7, 2024, 10:04 PM

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yes

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so

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you do log_2(...) on both sides

vernal phoenixBOT Apr 7, 2024, 10:05 PM

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𝔸dωn𝓲²s

naive pecan Apr 7, 2024, 10:05 PM

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so far so good?

obsidian rain Apr 7, 2024, 10:05 PM

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so if it was 3 it would be log 3

naive pecan Apr 7, 2024, 10:05 PM

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yes

obsidian rain Apr 7, 2024, 10:05 PM

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its just log and the base

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ok epix

naive pecan Apr 7, 2024, 10:05 PM

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yes

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Next we can make use of this property: $\log(x^a) = a\log(x)$

vernal phoenixBOT Apr 7, 2024, 10:06 PM

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𝔸dωn𝓲²s

obsidian rain Apr 7, 2024, 10:07 PM

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what would be the a in this case

naive pecan Apr 7, 2024, 10:07 PM

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the exponent

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2 to the power 0.15x

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we can drag out 0.15x

obsidian rain Apr 7, 2024, 10:08 PM

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so like 0.15log2 or something idk

vernal phoenixBOT Apr 7, 2024, 10:08 PM

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𝔸dωn𝓲²s

naive pecan Apr 7, 2024, 10:08 PM

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Now another fun fact.

vernal phoenixBOT Apr 7, 2024, 10:09 PM

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𝔸dωn𝓲²s

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𝔸dωn𝓲²s

naive pecan Apr 7, 2024, 10:09 PM

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So what'd you get here?

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log_2(2) is what?

obsidian rain Apr 7, 2024, 10:11 PM

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do i multiply the 2s or add log to it im confused

naive pecan Apr 7, 2024, 10:11 PM

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vernal phoenix **𝔸dωn𝓲²s**

read this again.

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what is log_2(2) according to this other property now?

obsidian rain Apr 7, 2024, 10:11 PM

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so 1

naive pecan Apr 7, 2024, 10:11 PM

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yes

vernal phoenixBOT Apr 7, 2024, 10:12 PM

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𝔸dωn𝓲²s

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𝔸dωn𝓲²s

naive pecan Apr 7, 2024, 10:12 PM

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Last step?

obsidian rain Apr 7, 2024, 10:13 PM

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do we have to put the f^-1(x) or something

naive pecan Apr 7, 2024, 10:13 PM

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not yet

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0.15

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we wanna get rid of that too

obsidian rain Apr 7, 2024, 10:14 PM

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can we divide

naive pecan Apr 7, 2024, 10:14 PM

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yes

obsidian rain Apr 7, 2024, 10:15 PM

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so just put that on the left and = x

vernal phoenixBOT Apr 7, 2024, 10:15 PM

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𝔸dωn𝓲²s

obsidian rain Apr 7, 2024, 10:15 PM

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ohhh

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ok

naive pecan Apr 7, 2024, 10:15 PM

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done.

obsidian rain Apr 7, 2024, 10:16 PM

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lemme go over the steps again i wanna see if i can get the same

obsidian rain Apr 7, 2024, 10:17 PM

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naive pecan So we can first divide by 17

why here couldnt we just subtract 17 from both sides btw

naive pecan Apr 7, 2024, 10:17 PM

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because 17 is being multiplied

obsidian rain Apr 7, 2024, 10:17 PM

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ok thanjs

naive pecan Apr 7, 2024, 10:17 PM

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so the anti-operation is division

obsidian rain Apr 7, 2024, 10:18 PM

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yeah i had the feeling just was confused a lil

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ok i got it

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nice

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thanks

brisk impBOT Apr 7, 2024, 10:22 PM

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obsidian rain thanks

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obsidian rain Apr 7, 2024, 10:23 PM

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.close

#Inverse and Domain