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wu :: forums    riddles    medium (Moderators: william wu, Icarus, Eigenray, SMQ, ThudnBlunder, towr, Grimbal)    geometric progression « Previous topic | Next topic » Pages: 1  Reply Notify of replies Send Topic Print    Author  Topic: geometric progression  (Read 1071 times) Christine Full Member     Posts: 159 geometric progression   « on: Apr 12th, 2013, 9:28am » Quote Modify For what number pairs x, y will the numbers     x, xlogx,  ylogy and (xy)log(xy)   be consecutive terms of a geometric progression? IP Logged SMQ wu::riddles Moderator Uberpuzzler     Gender: Posts: 2084 Re: geometric progression   « Reply #1 on: Apr 12th, 2013, 11:35am » Quote Modify One necessary (but not sufficient) condition: x1 + log y = y-log x   --SMQ IP Logged --SMQ pex Uberpuzzler     Gender: Posts: 880 Re: geometric progression   « Reply #2 on: Apr 12th, 2013, 2:08pm » Quote Modify I find only three solutions: (x,y) = (1,1) or ( exp((1 (+/-) sqrt(3)) / 4) , exp(-1/2) ), assuming the "log"s are natural logs. Hint: your numbers are in geometric progression if and only if their logs are in arithmetic progression. « Last Edit: Apr 12th, 2013, 2:12pm by pex » IP Logged Pages: 1  Reply Notify of replies Send Topic Print Forum Jump: ----------------------------- riddles -----------------------------  - easy => medium   - hard   - what am i   - what happened   - microsoft   - cs   - putnam exam (pure math)   - suggestions, help, and FAQ   - general problem-solving / chatting / whatever ----------------------------- general -----------------------------  - guestbook   - truth   - complex analysis   - wanted   - psychology   - chinese « Previous topic | Next topic »

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