Difference between revisions of "1950 AHSME Problems/Problem 42"
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==Solution== | ==Solution== | ||
| − | {{ | + | |
| + | Taking the log, we get <math>\log_x 2 = x^{x^{x}}... = 2</math>, and <math>\log_x 2 = 2</math>. Solving for x, we get <math>2=x^2</math>, and <math>\sqrt{2}=x \Rightarrow \mathrm{(D)}</math> | ||
==See Also== | ==See Also== | ||
Revision as of 08:20, 4 May 2012
Problem
The equation $x^{x^{x}}...\equal{}2$ (Error compiling LaTeX. Unknown error_msg) is satisfied when 
is equal to:
![$\textbf{(A)}\ \infty \qquad \textbf{(B)}\ 2 \qquad \textbf{(C)}\ \sqrt[4]{2} \qquad \textbf{(D)}\ \sqrt{2} \qquad \textbf{(E)}\ \text{None of these}$](http://latex.artofproblemsolving.com/f/a/c/faceac5e5369ac6f7869a0600488ed0d14885599.png)
Solution
Taking the log, we get 
, and 
. Solving for x, we get 
, and 
See Also
| 1950 AHSC (Problems • Answer Key • Resources) | ||
| Preceded by Problem 41 |
Followed by Problem 43 | |
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| All AHSME Problems and Solutions | ||
