Question

solve answer this question​

Answer 1

Answer:

x= -2 and x= -1

Step-by-step explanation:

2^x+3 can be rewritten as 2^x * 2^3

2^3 is 8

2^-x can be rewritten as 1/2^x

Therefore 2^x+3 + 2^-x can be rewritten as

2^x * 8 + 1/2^x = 6

Substitute 2^x into y therefore we rewrite the solution as

y * 8 + 1/y =6

8y + 1/y = 6

Move 6 to the left

8y + 1/y - 6 = 0

Multiply by y

8y^2 -6y + 1 = 0

Use quadratic equation

(attached file)

format: ax^2 + bx + c

so a= 8 b= -6 c= 1

which will result in y = 1/4 and y= 1/2

Since y = 2^x

2^x = 1/4 and 2^x = 1/2

Use log

$Log_{2}\frac{1}{2}$ = x and $Log_{2}\frac{1}{4}$= x

Therefore x = -1 and x = -2