Question

What is the value of n in the equation below?

Answer 1

option C

12

Explanation:

Given in the question an expression

`(a^(n) )/(a^(3) )=a^(9)`

To solve for n we will use rules of exponent

cross multiply

`a^(n)=a^(9)a^(3)`

apply product rule

`a^(n)=a^(9+3)`

`a^(n)=a^(12)`

Apply logarithm on both sides of equation

`lna^(n)=lna^(12)`

apply power rule of logarithm

nln(a) = 12ln(a)

ln(a) will cancel out on each side so we are left with

n= 12

Answer 2

12

Explanation:

We can use the property of exponents
`(a^b)/(a^c)=a^(b-c)` over here.

Let's use this property to write:

`(a^n)/(a^3)\\=a^(n-3)`

This is equal to a^9, hence, n - 3 = 9. Let's solve for n:

`n-3=9\\n=9+3\\n=12`

n = 12