SOLUTION: Please help me...i really do not understand how to solve for these answers. I have just tried plugging in different numbers and they were all wrong. I thought for sure that they wo

Algebra ->  Real-numbers -> SOLUTION: Please help me...i really do not understand how to solve for these answers. I have just tried plugging in different numbers and they were all wrong. I thought for sure that they wo      Log On


   

Question 350166: Please help me...i really do not understand how to solve for these answers. I have just tried plugging in different numbers and they were all wrong. I thought for sure that they would be close to 0 but I can't seem to find anything that works.
Find two natural numbers a and b such that b > a and
a^b = b^a.
Then a = ___
and b=___
Hint: It is not usually true that a^b = b^a.
Found 2 solutions by Alan3354, CharlesG2:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
2^4 = 4^2 is one set

Answer by CharlesG2(834) About Me  (Show Source):
You can put this solution on YOUR website!
Please help me...i really do not understand how to solve for these answers. I have just tried plugging in different numbers and they were all wrong. I thought for sure that they would be close to 0 but I can't seem to find anything that works.
Find two natural numbers a and b such that b > a and
a^b = b^a.
Then a = ___
and b=___
Hint: It is not usually true that a^b = b^a.


natural numbers are the counting numbers 1,2,3,4,5,6,...

answer is a = 2, and b = 4
here b > a since 4 > 2
a^b = 2^4 = 16
b^a = 4^2 = 16
a^b = b^a = 16

a b a^b b^a a^b=b^a
1 2 1 2
1 3 1 3
1 4 1 4
1 5 1 5
1 6 1 6
1 7 1 7
1 8 1 8
1 9 1 9
1 10 1 10
2 3 8 9
2 4 16 16 yes
2 5 32 25
2 6 64 36
2 7 128 49
2 8 256 64
2 9 512 81
2 10 1024 100
3 4 81 64
3 5 243 125
3 6 729 216
3 7 2187 343
3 8 6561 512
3 9 19683 729
3 10 59049 1000
4 5 1024 625
4 6 4096 1296
4 7 16384 2401
4 8 65536 4096
4 9 262144 6561
4 10 1048576 10000
5 6 15625 7776
5 7 78125 16807
5 8 390625 32768
5 9 1953125 59049
5 10 9765625 100000
6 7 279936 117649
6 8 1679616 262144
6 9 10077696 531441
6 10 60466176 1000000
7 8 5764801 2097152
7 9 40353607 4782969
7 10 282475249 10000000
8 9 134217728 43046721
8 10 1073741824 100000000
9 10 3486784401 1000000000