CEMC Euclid, 2007

Algebra Difficulty 3.0 AMC 10/12 Prove it Canada

Determine all values of $x$ for which $(\sqrt{x})^{\log_{10} x}=100$ .

We don't reproduce this publisher's solutions. Their own solution is here — work the problem first.

Want a route through all this instead of an archive? The track puts 2,604 problems in a working order, from Junior Challenge level to the IMO shortlist.

Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project. Solutions are the publisher's, linked not copied.