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1994 AHSME Problems/Problem 3

Revision as of 20:23, 27 June 2014 by TheMaskedMagician (talk | contribs) (Created page with "==Problem== How many of the following are equal to <math>x^x+x^x</math> for all <math>x>0</math>? <math>\textbf{I:}\ 2x^x \qquad\textbf{II:}\ x^{2x} \qquad\textbf{III:}\ (2x)^x ...")
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Problem

How many of the following are equal to $x^x+x^x$ for all $x>0$?

$\textbf{I:}\ 2x^x \qquad\textbf{II:}\ x^{2x} \qquad\textbf{III:}\ (2x)^x \qquad\textbf{IV:}\ (2x)^{2x}$

$\textbf{(A)}\ 0 \qquad\textbf{(B)}\ 1 \qquad\textbf{(C)}\ 2 \qquad\textbf{(D)}\ 3 \qquad\textbf{(E)}\ 4$

Solution

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