Answer:
f(9) = 2
Step-by-step explanation:
To know what if f(9), we need to replace x by 9 on the equation of f(x), so:
![\begin{gathered} f(x)=\log _3x \\ f(9)=\log _39 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/z8k17wbfvwxfs99p47x6z1biyppr0dv1ca.png)
Then, the logarithm needs the number at which 3 to the power of this number is equal to 9.
Therefore:
![f(9)=\log _39=2](https://img.qammunity.org/2023/formulas/mathematics/college/a8sepaiygu3s3taw4wkrulilui213nv62g.png)
Because:
![3^2=9](https://img.qammunity.org/2023/formulas/mathematics/high-school/4sid5au9qtxmz9me94k68s2539uyhme2gp.png)
So, the answer is:
f(9) = 2