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I am terrible with Logs plz help

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\[f(x) = \log_{3}(\sqrt(x) + 3 \ \]
Log base 3 square root x plus 3
How do you find the inverse of this/

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start with the fact that \(\log_3(\sqrt{x})=\frac{1}{2}\log_3(x)\)
is it the log of the whole thing?
No just log base 3 square root x
i mean is it \[f(x)=\log_3(\sqrt{x}+3)\] or \[f(x)=\log_3(\sqrt{x})+3\]
2nd one
ok then start with \[f(x)=\frac{1}{2}\log_3(x)+3\]
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 \(y\)
you need the steps?
Yes please . I always get confused when there's stuff like log base 3
1) subtract 3 2) multiply by 2 3) raise 3 to everything
\[x=\frac{1}{2}\log_3(y)+3\] \[x-3=\frac{1}{2}\log_3(y)\] \[2x-6=\log_3(y)\] \[3^{2x-6}=y\]
last step because \[\log_b(y)=x\iff b^x=y\]
Ohhh!!! Thank you so much !

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