Question 1199910
<br>
{{{2^(a+1)+2^a=3^(b+2)-3^b}}}<br>
Simplify using greatest common factors on both sides:<br>
{{{(2^a)(2^1+1)=(3^b)(3^2-1)}}}
{{{(2^a)(3)=(3^b)(8)}}}
{{{(2^a)(3^1)=(3^b)(2^3)}}}<br>
Both expressions are prime factorizations, so the exponents on like prime factors must be the same: a=3 and b=1<br>
ANSWER: (a,b) = (3,1)<br>
CHECK:
2^4+2^3 = 16+8 = 24
3^3-3^1 = 27-3 = 24<br>