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2 June, 12:48

In the equation 9^2 x 27^3 = 3^x, what is the value of x?

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  1. 2 June, 14:48
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    x=13

    Step-by-step explanation:

    9^2 * 27^3 = 3^x

    We need to get each term with a base of 3

    9^2 = (3^2) ^2

    We know that a^b^c = a^ (b*c)

    (3^2) ^2 = 3^ (2+2) = 3^4

    27^3 = (3^3) ^3 = 3^ (3*3) = 3^9

    Replacing these in the original equation

    3^4 * 3^9 = 3^x

    We know that a^b * a^c = a^ (b+c)

    3^4 * 3^9 = 3^ (4+9) = 3^13 = 3^x

    The bases are the same, so the exponents must be the same

    x=13
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