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1 July, 13:26

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?

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  1. 1 July, 13:45
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    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
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