Question

$log_{a}(1024) = 20$
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Answer 1

$log_{_a}1024~=~20\\\\\\1024~=~a^20\\\\\\2^{10}~=~a^{20}\\\\\\2^{10}~=~\left(a^2\right)^{10}\\\\\\2~=~a^2\\\\\\\boxed{a~=~\sqrt[]{2}}$