2^(cos2x) +2^(cos^2 x) =3×2^(−cos2x) x=...? i′m so sorry, it′s my mistake, the true question is 2^(cos2x) +2^(cos^2 x) =3×2^(−cos2π)


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Question Number 10429 by ridwan balatif last updated on 09/Feb/17

$2^{\cos 2 x} + 2^{\cos^{2} x} = 3 \times 2^{- \cos 2 x}$ $x = . . . ?$ $i^{'} m so sorry, {it}^{'} s my mistake, the true question is$ $2^{\cos 2 x} + 2^{\cos^{2} x} = 3 \times 2^{- \cos 2 π}$
	Answered by arge last updated on 09/Feb/17

	$l o g 2^{c o s 2 x} + l o g 2^{{c o s}^{2} x} = l o g (3 \times 2^{- c o s 2 x})$ $l o g (2^{c o s 2 x} 2^{{c o s}^{2} x}) = l o g 3 + l o g 2^{- c o s 2 x}$ $l o g (2^{c o s 2 x} 2^{{c o s}^{2} x}) - l o g 2^{- c o s 2 x} = l o g 3$ $l o g [(2^{c o s 2 x} 2^{{c o s}^{2} x}) / 2^{- c o s 2 x}] = l o g 3$ $l o g [(2^{c o s 2 x} 2^{{c o s}^{2} x}) / 2^{- c o s 2 x}] = 0.48$ $2^{c o s 2 x + {c o s}^{2} x + c o s 2 x} = 3$ $2^{{c o s}^{2} x + 2 c o s 2 x} = 3$ ${c o s}^{2} x + 2 c o s 2 x = 1.58$ ${c o s}^{2} x + 2 {c o s}^{2} x - 2 {s e n}^{2} x = 1.58$ $3 {c o s}^{2} x - 2 + 2 {c o s}^{2} x = 1.58$ $5 {c o s}^{2} x = 3.58$ $c o s x = 0.85$ $x = 32 . 20^{°}$
	Commented by amir last updated on 09/Feb/17

	$h e l l o . d e a r . y o u r m e t h o d i s n o t c o r r e c t .$ $y o u a p p l y t h e l o g i n w r o n g f o r m u l a .$ $l o g (a + b) \neq l o g a \times l o g b$
	Commented by arge last updated on 10/Feb/17

	$t h a n k y o u . R e c a l l s {N A S A}^{'} s m i s t a k e .$
	Answered by sandy_suhendra last updated on 08/Feb/17

	$2^{\cos 2 x} + 2^{\frac{\cos 2 x + 1}{2}} = \frac{3}{2^{\cos 2 x}}$ $2^{\cos 2 x} + \sqrt{2^{\cos 2 x} . 2} = \frac{3}{2^{\cos 2 x}}$ $misalkan 2^{\cos 2 x} = a$ $a + \sqrt{2 a} = \frac{3}{a}$ $\sqrt{2 a} = \frac{3}{a} - a$ $2 a = {(\frac{3}{a} - a)}^{2}$ $2 a = \frac{9}{a^{2}} - 6 + a^{2}$ ${2 a}^{3} = 9 - {6 a}^{2} + a^{4}$ $a^{4} - {2 a}^{3} - {6 a}^{2} + 9 = 0$ $maaf, cuma baru bisa sampai langkah ini$
	Commented by amir last updated on 09/Feb/17

	Commented by amir last updated on 09/Feb/17

	$a = 1.13$ $2^{\cos 2 x} = 1.13 \Rightarrow \cos 2 x = \log_{2} 1.13 = . 176$ $2 x = \cos^{- 1} . 176 = 1.39 \Rightarrow x = \frac{1}{2} \cos^{- 1} (. 176) + k π, k \in Z$
	Answered by amir last updated on 09/Feb/17

	$2^{\cos 2 x} = a \Rightarrow a + \sqrt{2 a} = \frac{3}{2}$ $2 \sqrt{2 a} = 3 - 2 a \Rightarrow 8 a = 9 - 12 a + 4 a^{2}$ $4 a^{2} - 20 a + 9 = 0 \Rightarrow a = \frac{20 \pm \sqrt{20^{2} - 4 \times 4 \times 9}}{2 \times 4} =$ $a = \frac{20 \pm 16}{8} \Rightarrow a = \frac{1}{2}, \frac{9}{2}$ $2^{\cos 2 x} = \frac{1}{2} \Rightarrow \cos 2 x = - 1 = \cos π$ $2 x = π + 2 k π \Rightarrow x = \frac{π}{2} + k π, k \in Z$ $2^{\cos 2 x} = \frac{9}{2} \Rightarrow \cos 2 x = \log_{2} 9 = 2 \log_{2} 3 + 1 > 1 .$
	Commented by ridwan balatif last updated on 09/Feb/17

	$terimakasih bantuannya, setidaknya udah$ $dapat gambaran penyelesaiannya$
	Commented by amir last updated on 09/Feb/17

	$t h e p r o b l e m w a s f i x e d b y s e n d e r a s$ $b e l o w :$ $2^{\cos 2 x} + 2^{\cos^{2} x} = 3 \times 2^{- c o s 2 π}$ $s o : a + \sqrt{2 a} = \frac{3}{2}$ $b u t i s o l v e d t h i s c a s e i n d i f f e r e n t p o s t .$
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