Question

Choose the correct answer: if 2^2n-1=(1/8^n-3) then the value of n is a. 3 b. 2 c. 0 d. -2

Answer 1

Answer:n equals 2

Step-by-step explanation:

Given equation

2^2n-1=(1/8)^n-3

or, 2^2n-1=2^(-3) (n-3)

Because

(1/8)^n-3= (1/2)^3^(n-3)=2^-1^3^(n-3)

= 2^-3n+9

Now

2^-3n+9=2^2n+1

Therefore

-3n+9=2n+1

5n=10

n=2

Answer 2

b. 2

The value of n is 2 .

Explanation:

The given equation is : $2^{2n-1}=(\dfrac{1}{8^{n-3}})$

Since $8= 2^3$

So ,  $2^{2n-1}=(\dfrac{1}{(2^3)^{n-3}})$

Also, $(a^m)^n= a^{mn}$   [Properties of exponent.]

So our expression will become

 $2^{2n-1}=(\dfrac{1}{2^{3(n-3)}})$

Also, $\dfrac{1}{a^m} =a^{-m}$   [Properties of exponent.]

So , our expression will become

$2^{2n-1}=2^{-3(n-3)}$

$\Rightarrow\ 2n-1=-3(n-3)$       [$\because a^m=a^n \Rightarrow\ m=n$]

$\Rightarrow\ 2n-1=-3n+9$    

$\Rightarrow\ 2n+3n=9+1$    

$\Rightarrow\ 5n=10\Rightarrow\ n=2$    

So , the value of n is 2 .

Hence, the correct answer is b. 2 .

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