Question

I am terrible with Logs plz help

Answer 1

\[f(x) = \log_{3}(\sqrt(x) + 3 \ \]

Answer 2

Log base 3 square root x plus 3

Answer 3

How do you find the inverse of this/

Answer 4

start with the fact that \(\log_3(\sqrt{x})=\frac{1}{2}\log_3(x)\)

Answer 5

is it the log of the whole thing?

Answer 6

No just log base 3 square root x

Answer 7

i mean is it
\[f(x)=\log_3(\sqrt{x}+3)\] or
\[f(x)=\log_3(\sqrt{x})+3\]

Answer 8

2nd one

Answer 9

ok then start with
\[f(x)=\frac{1}{2}\log_3(x)+3\]

Answer 10

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 \(y\)

Answer 11

you need the steps?

Answer 12

Yes please . I always get confused when there's stuff like log base 3

Answer 13

1) subtract 3
2) multiply by 2
3) raise 3 to everything

Answer 14

\[x=\frac{1}{2}\log_3(y)+3\]
\[x-3=\frac{1}{2}\log_3(y)\]
\[2x-6=\log_3(y)\]
\[3^{2x-6}=y\]

Answer 15

last step because
\[\log_b(y)=x\iff b^x=y\]

Answer 16

Ohhh!!! Thank you so much !

Answer 17

yw