if x>0, x^2=2^64 and x^x=2^y what is the value of y?
\(x^2=2^{64}\) square root
\(\sqrt{x^2}=\sqrt{2^{64}}\) calculate
\(x=2^{32}\) result for x
\(\large x^x=2^y\) output equation. x-value
\(\large x^x=(2^{32})^{2^{32}}=2^{32\times 2^{32}}=2^{2^5\times 2^{32}}=2^{2^{37}}=2^y\)
\(\large2^{2^{37}}=2^y\) output equation. x is used
If the basis of two powers is equal, the exponents are equal.
\(\large y={2^{37}} \)
\(y=137438953472\)
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\(\large x^x=2^y\) output equation. x and y used
\(\Large(2^{32})^{(2^{32})}=2^{137438953472}\) x and y used. calculate
\(\large32\times2^{32}=137438953472\) q.e.d
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