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What is the value of x given that `2*4^(4*log_4 x) = 486`

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needyourhelp | Student, Kindergarten | eNoter

Posted May 23, 2012 at 4:57 PM via web

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What is the value of x given that `2*4^(4*log_4 x) = 486`

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted May 23, 2012 at 5:04 PM (Answer #1)

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The equation `2*4^(4*log_4 x) = 486` has to be solved for x.

`2*4^(4*log_4 x) = 486`

=> `4^(4*log_4 x) = 243`

=> `4^(log_4 x^4) = 243`

Use the property `a^(log_a b) = b`

=> `x^4 = 243`

=> `x = 3*root(4) 3`

The solution of the equation is `x = 3*root(4) 3`

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