SOLUTION: Solve in integer numbers 2^(x+1) + 2^x = 3^(y+2) - 3^y

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Question 1189535: Solve in integer numbers 2^(x+1) + 2^x = 3^(y+2) - 3^y

Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52921)   (Show Source): You can put this solution on YOUR website!
.
Solve in integer numbers 2^(x+1) + 2^x = 3^(y+2) - 3^y
~~~~~~~~~~~~~~~~~ 

Left  side of the given equation is  2*2^x + 2^x = 3*2^x.

Right side of the given equation is  9*3^y + 3^y = 8*3^y.


So, the given equation is

    3*2^x = 2^3*3^y.


Due to uniqueness of decomposition integer numbers into the product of prime numbers, 
from the last equation we conclude

    x = 3,  y = 1.


ANSWER.  x = 3;  y = 1.

Solved.



Answer by greenestamps(13216)   (Show Source): You can put this solution on YOUR website!

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