Mystery exponent

Algebra Level 1

{ 314 }^{ a }=\quad \sqrt [ 222 ]{ 314 }

Find the value of a.


The answer is 0.0045.

Jake Maason by Jake Maason , 28, USA

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1 solution

Jake Maason
Dec 28, 2014

314 a = 314 222 ( 31 4 a ) 222 = ( 314 222 ) 222 314 a 222 = 31 4 1 t h u s a 222 = 1 → a = 1 222 { 314 }^{ a }=\sqrt [ 222 ]{ 314 } \\ (314^{ a })^{ 222 }=\quad (\sqrt [ 222 ]{ 314 } )^{ 222 }\\ { 314 }^{ a222 }=314^{ 1 }\\ thus\quad a222\quad =\quad 1\quad \rightarrow \quad a\quad =\quad \frac { 1 }{ 222 }

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