What is the answer to 2^x+1/(2^x)=2 ?

The answer to 2^x+1/(2^x)=2 is x=0

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2^x+1/(2^x)=2

2^{x} + \frac{1}{2 ^{x}} = 2

x = 0

Solution steps

2^{x} + \frac{1}{2 ^{x}} = 2

Apply exponent rules

2^{x} + (2^{x})^{- 1} = 2

Rewrite the equation with

2^{x} = u

u + (u)^{- 1} = 2

Solve

u + u^{- 1} = 2 : u = 1

u = 1

Substitute back

u = 2^{x},

solve for

x

Solve

2^{x} = 1 : x = 0

x = 0

Verify Solutions:

x = 0

True

The solution is

x = 0

9^{- x} = 3^{x + 2}

7^{2 x + 3} = 7^{3 x - 4}

x, x^{y} = e^{x - y}

3^{x + 1} = 729

1 0^{2 x + 6} = 243