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243^(.2x)= 81^(x+5)

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    both 243 and 81 are powers of 3
    243 = 3^5 and 81 = 3^4

    so rewrite your equation:

    243^(.2x)= 81^(x+5)
    (3^5)^(.2x) = (3^4)^(x+5)
    3^x = 3^(4z+20)

    If the bases are the same, for the equation to be true, obviously the exponents have to be the sam

    so x = 4x+20
    x = -20/3

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