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Question Number 193356 by leandrosriv02 last updated on 11/Jun/23

	Answered by deleteduser1 last updated on 11/Jun/23

	$m = 4$ $\frac{d}{d m} 3^{m} = 3^{m} I n (3) > \frac{d}{d m} (2^{m} + 65) = 2^{m} I n (2) (w h e n m > 0)$ $S o, t h e r e e x i s t s n o o t h e r s o l u t i o n a f t e r t h e i r$ $i n t e r s e c t i o n a t x = 4$ $S u p p o s e m ⩽ 0, {w e}^{^{'}} d h a v e 3^{m} - 2^{m} ⩽ 0 < 65$ $\Rightarrow m > 0 a n d o n l y s o l u t i o n i s m = 4$
	Answered by qaz last updated on 11/Jun/23
	$m=2t (3^t +2^t )(3^t −2^t )=65=5×13 ⇒ { ((3^t +2^t =13)),((3^t −2^t =5)) :}⇒3^t =9 ,2^t =4 ⇒t=2 , m=4$
	$m = 2 t$ $(3^{t} + 2^{t}) (3^{t} - 2^{t}) = 65 = 5 \times 13$ $\Rightarrow {\begin{cases} 3^{t} + 2^{t} = 13 \\ 3^{t} - 2^{t} = 5 \end{cases} \Rightarrow 3^{t} = 9, 2^{t} = 4$ $\Rightarrow t = 2, m = 4$
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