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Algebra Level pending

If 1 6 x + 1 6 x 1 = 10 16^x + 16^{x - 1} = 10 , find 17 ( 2 4 x ) 17(2^{4x}) .


The answer is 160.

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1 solution

Satwik Murarka
May 12, 2016

16^x + 16^x-1 = 10

We take 16^x common,

16^x(1+16^-1) =10

16^x(1+1÷16)=10

16^x(17/16)=10

16^x can also be written as, 2^4x

2^4x×17/16=10

17×2^4x =16×10=160

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