Math Question and Answers


Question and Answers Forum

All Questions Topic List
Algebra Questions
Previous in All Question Next in All Question
Previous in Algebra Next in Algebra
Question Number 68234 by Mikael last updated on 07/Sep/19

Commented by kaivan.ahmadi last updated on 07/Sep/19
$3^(x+(1/2)) +3^(x−(1/2)) =4^x +2^(2x−1) ⇒ 3^(x−(1/2)) (3+1)=2^(2x−1) (2+1)⇒ (2^(2x−1) /3^(x−(1/2)) )=(4/3)⇒(2^(2x−1) /4)=(3^(x−(1/2)) /3)⇒2^(2x−3) =3^(x+(1/2)) ⇒ { ((2x−3=0⇒x=(3/2))),((x+(1/2)=0⇒x=−(1/2))) :} x=(3/2) is answer$
$3^{x + \frac{1}{2}} + 3^{x - \frac{1}{2}} = 4^{x} + 2^{2 x - 1} \Rightarrow$ $3^{x - \frac{1}{2}} (3 + 1) = 2^{2 x - 1} (2 + 1) \Rightarrow$ $\frac{2^{2 x - 1}}{3^{x - \frac{1}{2}}} = \frac{4}{3} \Rightarrow \frac{2^{2 x - 1}}{4} = \frac{3^{x - \frac{1}{2}}}{3} \Rightarrow 2^{2 x - 3} = 3^{x + \frac{1}{2}} \Rightarrow$ ${\begin{cases} 2 x - 3 = 0 \Rightarrow x = \frac{3}{2} \\ x + \frac{1}{2} = 0 \Rightarrow x = - \frac{1}{2} \end{cases}$ $x = \frac{3}{2} i s a n s w e r$
Commented by Mikael last updated on 07/Sep/19

$t h a n k s$
Commented by Prithwish sen last updated on 08/Sep/19

$2^{2 x} = a 3^{x} = b$ $a - \frac{b}{\sqrt{3}} = \sqrt{3} b - \frac{a}{2}$ $\frac{3 a}{2} = \frac{4 b}{\sqrt{3}}$ $\frac{a}{b} = \frac{2^{3}}{3^{\frac{3}{2}}}$ $∴ 2 x = 3 \Rightarrow x = \frac{3}{2}$
Commented by Rasheed.Sindhi last updated on 09/Sep/19
$Sir kaivan ahmadi I don′t understand 2^(2x−3) =3^(x+(1/2)) ⇒^(?) { ((2x−3=0⇒x=(3/2))),((x+(1/2)=0⇒x=−(1/2))) :}$
$Sir kaivan ahmadi I {don}^{'} t understand$ $2^{2 x - 3} = 3^{x + \frac{1}{2}} \overset{?}{\Rightarrow} {\begin{cases} 2 x - 3 = 0 \Rightarrow x = \frac{3}{2} \\ x + \frac{1}{2} = 0 \Rightarrow x = - \frac{1}{2} \end{cases}$
Commented by kaivan.ahmadi last updated on 13/Sep/19

$s i n c e 2^{0} = 3^{0}$ $o t h e r w i s e t h i s e q u a l i t y i s n o t t r u e .$
	Answered by Rasheed.Sindhi last updated on 09/Sep/19

	$4^{x} + 4^{x - \frac{1}{2}} = 3^{x + \frac{1}{2}} + 3^{x - \frac{1}{2}}$ $4^{x - \frac{1}{2}} (4^{\frac{1}{2}} + 1) = 3^{x - \frac{1}{2}} (3 + 1)$ $4^{x - \frac{1}{2} - 1} = 3^{x - \frac{1}{2} - 1}$ $\frac{4^{x - \frac{3}{2}}}{3^{x - \frac{3}{2}}} = 1$ ${(\frac{4}{3})}^{x - \frac{3}{2}} = {(\frac{4}{3})}^{0}$ $x - \frac{3}{2} = 0$ $x = \frac{3}{2}$
Terms of Service
Privacy Policy
Contact: info@tinkutara.com

Question and Answers Forum