Sure, let's solve the given equation step by step:
The given equation is:
[tex]\[ 2^n \times 4 = \frac{1}{2^n} \times 8 \][/tex]
First, rewrite the right side of the equation:
[tex]\[ \frac{1}{2^n} \times 8 = \frac{8}{2^n} \][/tex]
Now, the equation becomes:
[tex]\[ 2^n \times 4 = \frac{8}{2^n} \][/tex]
Next, multiply both sides of the equation by [tex]\( 2^n \)[/tex] to eliminate the fraction:
[tex]\[ 2^n \times 4 \times 2^n = 8 \][/tex]
Since [tex]\( 2^n \times 2^n = 2^{2n} \)[/tex], we can simplify this to:
[tex]\[ 4 \times 2^{2n} = 8 \][/tex]
Next, divide both sides by 4:
[tex]\[ 2^{2n} = 2 \][/tex]
Since the bases are the same, we can set the exponents equal to each other:
[tex]\[ 2n = 1 \][/tex]
Finally, solve for [tex]\( n \)[/tex]:
[tex]\[ n = \frac{1}{2} \][/tex]
So, the value of [tex]\( n \)[/tex] is:
[tex]\[ n = 0.5 \][/tex]
