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What is the value of n in the equation below?

What is the value of n in the equation below?-example-1
User Bmd
by
5.7k points

2 Answers

6 votes

Answer:

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

User Rohitvats
by
5.3k points
3 votes

Answer:

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

User Nirup Iyer
by
5.1k points
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