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. 



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