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If x^x^x^∞ = 3, then value of x is:Please solve this wonderful question...
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You need to solve for `x` the equation `((x^x)^x)^oo = 3` using limits and the properties of exponentials, such that:
`lim_(x->oo) x^(x*x*oo) = lim_(x->oo) x^oo `
`=> lim_(x->oo) x^oo = 3 `
`x = lim_(x->oo) (3^(1/oo)) => x = 3^lim_(x->oo) (1/oo)`
`x = 3^0 => x = 1`
Hence, evaluating x using limits and the properties of exponentials, yields `x = 3^(1/oo) = root(oo)(3) => x = 1.`
Posted by sciencesolve on January 16, 2013 at 5:59 PM (Answer #1)
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