2^2x  + 2^(x+2)  - 4 * 2^3=0

Asked by malvika7m | 15th May, 2016, 02:38: PM

Expert Answer:

C o n s i d e r space t h e space g i v e n space e q u a t i o n
2 to the power of 2 x end exponent plus 2 to the power of open parentheses x plus 2 close parentheses end exponent minus 4 cross times 2 cubed equals 0
U sin g space l a w s space o f space e x p o n e n t s comma space r e w r i t i n g space t h e space a b o v e space e q u a t i o n comma space w e space h a v e comma
open parentheses 2 squared close parentheses to the power of x plus 2 to the power of x cross times 2 squared minus 4 cross times 8 equals 0
rightwards double arrow open parentheses 2 to the power of x close parentheses squared plus 2 to the power of x cross times 4 minus 32 equals 0
S u b s t i t u t i n g space t h e space v a l u e space y equals 2 to the power of x comma space t h e space a b o v e space e q u a t i o n space b e c o m e s comma
rightwards double arrow y squared plus 4 y minus 32 equals 0
T h i s space i s space a space q u a d r a t i c space i n space y.
S o l v i n g space t h e space q u a d r a t i c space w e space h a v e comma
y squared plus 8 y minus 4 y minus 32 equals 0
rightwards double arrow y open parentheses y plus 8 close parentheses minus 4 open parentheses y plus 8 close parentheses equals 0
rightwards double arrow open parentheses y minus 4 close parentheses open parentheses y plus 8 close parentheses equals 0
rightwards double arrow y minus 4 equals 0 space o r space y plus 8 equals 0
rightwards double arrow y equals 4 space o r space y equals negative 8
y equals 4 space
rightwards double arrow 2 to the power of x equals 4
rightwards double arrow 2 to the power of x equals 2 squared
rightwards double arrow x equals 2
N e g l e c t i n g space t h e space n e g a t i v e space r o o t space y equals negative 8 comma space w e space h a v e comma space x equals 2

Answered by Vimala | 16th May, 2016, 11:17: AM

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