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Empower With X and 0.4 (Posted on 2008-03-10) Difficulty: 2 of 5
Determine all possible positive real numbers X that satisfy this equation:

X0.4X = 0.4X0.4

Note: For the purposes of the problem, abc is equal to a^(b^c)

See The Solution Submitted by K Sengupta    
Rating: 4.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re: computer exploration (spoiler) | Comment 2 of 7 |
(In reply to computer exploration (spoiler) by Charlie)

DEFDBL A-Z
df = .04
FOR x = df TO 1 STEP df
 a = x ^ (.4 ^ x): b = .4 ^ (x ^ .4)
 PRINT USING "##.#######"; x; a; b
NEXT
DO: LOOP UNTIL INKEY$ > ""
df = 3 / 45
FOR x = df TO 4 STEP df
 a = x ^ (.4 ^ x): b = .4 ^ (x ^ .4)
 PRINT USING "##.#######"; x; a; b
NEXT
DO: LOOP UNTIL INKEY$ > ""
df = 1
FOR x = df TO 40 STEP df
 a = x ^ (.4 ^ x): b = .4 ^ (x ^ .4)
 PRINT USING "##.#######"; x; a; b
NEXT
  Posted by Charlie on 2008-03-10 16:21:10

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