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If x^x^x^∞ = 3, then value of x is:Please solve this wonderful question...

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nasirjam | Student, Grade 9 | (Level 2) Honors

Posted January 16, 2013 at 9:39 AM via web

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If x^x^x^∞ = 3, then value of x is:

Please solve this wonderful question...

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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted January 16, 2013 at 5:59 PM (Answer #1)

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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.`

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