Question

3(2^x+1)-2^(x+2)+5=0

Answer 1

we have to solve the equations :

(i) $3(2^x+1)-2^{x+2}+5= 0$ and (ii) $3^x=9.3^y,8.2^y=4^x$

solution : 1. $3(2^x+1)-2^{x+2}+5=0$

⇒$3.2^x+3-2^x.2^2+5=0$

⇒$3.2^x-4.2^x+8=0$

⇒$-2^x+8=0$

⇒$2^x=8=2^3$

⇒x = 3

Therefore the value of x = 3.

2. $3^x=9.3^y,8.2^y=4^x$

case 1 : $3^x=9.3^y$

⇒$3^x=3^2.3^y$

⇒$3^x=3^{(y+2)}$

⇒x = y + 2

⇒x - y = 2 ........(1)

case 2 : $8.2^y=4^x$

⇒$2^3.2^y=2^{2x}$

⇒$2^{(y+3)}=2^{2x}$

⇒y + 3 = 2x

⇒2x - y = 3 .........(2)

from equations (1) and (2) we get,

x = 1 and y = -1

Answer 2

Answer:

Hope this will be helps you...