Question

The area of a square can be represented by the expression x10. The side of the square can be written in the form xn.

What is the value of n?

Answer 1

The answer is n = 5.

Area (A) of the square can be expressed as:
A = a²
where a is the side of the square.

It is given:
A = x¹⁰
a = xⁿ

Therefore
x¹⁰ = (xⁿ)² = xⁿ*²= x²ⁿ
x¹⁰ = x²ⁿ

Let's logarithm both sides of the equation:
log(x¹⁰) = log (x²ⁿ)
⇒ 10 * log(x) = 2n * log(x)

Divide both sides of the equation by log(x):
10 * log(x) / log(x) = 2n * log(x) / log(x)
10 * 1 = 2n * 1
10 = 2n
⇒ n = 10 ÷ 2 = 5