## 3psilon 2 years ago I am terrible with Logs plz help

1. 3psilon

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

2. 3psilon

Log base 3 square root x plus 3

3. 3psilon

How do you find the inverse of this/

4. satellite73

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

5. satellite73

is it the log of the whole thing?

6. 3psilon

No just log base 3 square root x

7. satellite73

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

8. 3psilon

2nd one

9. satellite73

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

10. satellite73

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 $$y$$

11. satellite73

you need the steps?

12. 3psilon

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

13. satellite73

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

14. satellite73

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

15. satellite73

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

16. 3psilon

Ohhh!!! Thank you so much !

17. satellite73

yw