Answer:
Option (a) is correct.
[tex]\log _3\left(9\right)=2[/tex]
Step-by-step explanation:
Given: [tex]\log_39[/tex]
We have to evaluate [tex]\log_39[/tex] and choose the correct from the given options.
Consider the given [tex]\log_39[/tex]
Rewrite 9 as power of 3 as [tex]9=3^2[/tex]
[tex]\log_39=\log _3\left(3^2\right)[/tex]
Apply log rule, [tex]\quad \log _a\left(x^b\right)=b\cdot \log _a\left(x\right)[/tex]
[tex]\log_3(3^2)=2\log _3\left(3\right)[/tex]
Apply log rule, [tex]\log _a\left(a\right)=1[/tex]
[tex]\log _3\left(3\right)=1[/tex]
Thus, [tex]2\log _3\left(3\right)=2[/tex]
Thus, [tex]\log _3\left(9\right)=2[/tex]
Thus, option (a) is correct.
