solve for n

E= 1/5 pix^2n

1 answer

To solve for n, we need to isolate it on one side of the equation.

First, let's simplify the equation:

E = (1/5) * pi * x^(2n)

Next, let's solve for n:

Divide both sides of the equation by (1/5) * pi * x^2:

E / (1/5) * pi * x^2 = x^2n

Now, we can use logarithms to solve for n. Take the logarithm (base 2) of both sides of the equation:

log2(E / (1/5) * pi * x^2) = log2(x^2n)

Apply the logarithm property log_b(x^n) = n * log_b(x):

log2(E / (1/5) * pi * x^2) = 2n * log2(x)

Now, divide both sides of the equation by 2 * log2(x):

log2(E / (1/5) * pi * x^2) / (2 * log2(x)) = n * log2(x) / (2 * log2(x))

On the right side of the equation, log2(x) / (2 * log2(x)) simplifies to 1/2:

log2(E / (1/5) * pi * x^2) / (2 * log2(x)) = n * 1/2

Simplify further:

n = log2(E / (1/5) * pi * x^2) / (2 * log2(x))