[tex]36^b=3 \ \ \ (1)\\
36^a=4\ \ \ \ (2)\\\;\\
4=\dfrac{36}{9}=\dfrac{36}{3^2}\stackrel{(1)}{=}\dfrac{36}{36^{2b}} \ \ \ (3)\\\;\\
(2),\ (3) \Longrightarrow 36^a=\dfrac{36}{36^{2b}} \Longrightarrow 36^a\cdot 36^{2b} =36\Longrightarrow 36^{a+2b} =36
\\\;\\
\Longrightarrow a+2b=1 \Longrightarrow 2b=1-a\ \ \ (4)
[/tex]
Evaluam exponentul lui 25 :
[tex]\dfrac{1-a-b}{1-a}\ \stackrel{(4)}{=} \ \dfrac{2b-b}{2b}=\dfrac{b}{2b}=\dfrac{1}{2}[/tex]
Deci, vom avea :
[tex]25^{\frac{1}{2}} =\sqrt{25} =5 \in \mathbb{N}[/tex]
