Answer:
option C
12
Explanation:
Given in the question an expression
![(a^(n) )/(a^(3) )=a^(9)](https://img.qammunity.org/2020/formulas/mathematics/middle-school/uhvtofqqhgie5h51s130vzm18ybsjaesyj.png)
To solve for n we will use rules of exponent
cross multiply
![a^(n)=a^(9)a^(3)](https://img.qammunity.org/2020/formulas/mathematics/middle-school/ob7sxl4byt08cvrssqxqofvc9zhpwhx1tu.png)
apply product rule
![a^(n)=a^(9+3)](https://img.qammunity.org/2020/formulas/mathematics/middle-school/6or7ekm1f6jm6d3q7wbdenhtuwhytfp37l.png)
![a^(n)=a^(12)](https://img.qammunity.org/2020/formulas/mathematics/middle-school/q94x6bu1yynlzz381jwp4elh8lhhi85ysr.png)
Apply logarithm on both sides of equation
![lna^(n)=lna^(12)](https://img.qammunity.org/2020/formulas/mathematics/middle-school/5s9ywuvgsgbrn9ntry5rxh1kly62n303x8.png)
apply power rule of logarithm
nln(a) = 12ln(a)
ln(a) will cancel out on each side so we are left with
n= 12