# Exp

If
$\sqrt[6]{ 102-62 } = \sqrt[n]{ 1024 }$
, then n is:

Result

n =  10

#### Solution:

$\sqrt[6]{ 10^2-6^2 } = \sqrt[n]{ 1024 } \ \\ \sqrt[6]{ 64 } = \sqrt[n]{ 1024 } \ \\ 2 = \sqrt[n]{ 1024 } \ \\ 2^{10} = 1024 \ \\ \ \\ n=10 \ \\ \ \\ n = \dfrac{ 6\cdot \log 1024}{ \log( 10^2-6^2) } = 10$

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