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3psilonBest ResponseYou've already chosen the best response.0
\[f(x) = \log_{3}(\sqrt(x) + 3 \ \]
 one year ago

3psilonBest ResponseYou've already chosen the best response.0
Log base 3 square root x plus 3
 one year ago

3psilonBest ResponseYou've already chosen the best response.0
How do you find the inverse of this/
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
start with the fact that \(\log_3(\sqrt{x})=\frac{1}{2}\log_3(x)\)
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
is it the log of the whole thing?
 one year ago

3psilonBest ResponseYou've already chosen the best response.0
No just log base 3 square root x
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
i mean is it \[f(x)=\log_3(\sqrt{x}+3)\] or \[f(x)=\log_3(\sqrt{x})+3\]
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
ok then start with \[f(x)=\frac{1}{2}\log_3(x)+3\]
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
we can do the usual trick of writing \[y=\frac{1}{2}\log_3(x)+3\]then \[x=\frac{1}{2}\log_3(y)+3\] and solve for \(y\)
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
you need the steps?
 one year ago

3psilonBest ResponseYou've already chosen the best response.0
Yes please . I always get confused when there's stuff like log base 3
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
1) subtract 3 2) multiply by 2 3) raise 3 to everything
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
\[x=\frac{1}{2}\log_3(y)+3\] \[x3=\frac{1}{2}\log_3(y)\] \[2x6=\log_3(y)\] \[3^{2x6}=y\]
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
last step because \[\log_b(y)=x\iff b^x=y\]
 one year ago

3psilonBest ResponseYou've already chosen the best response.0
Ohhh!!! Thank you so much !
 one year ago
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