What is the answer to 3^x+3^{1-x}=4 ?

The answer to 3^x+3^{1-x}=4 is x=1,x=0

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3^x+3^{1-x}=4

3^{x} + 3^{1 - x} = 4

x = 1, x = 0

Solution steps

3^{x} + 3^{1 - x} = 4

Apply exponent rules

3^{x} + (3^{x})^{- 1} \cdot 3^{1} = 4

Rewrite the equation with

3^{x} = u

u + (u)^{- 1} \cdot 3^{1} = 4

Solve

u + u^{- 1} \cdot 3^{1} = 4 : u = 3, u = 1

u = 3, u = 1

Substitute back

u = 3^{x},

solve for

x

Solve

3^{x} = 3 : x = 1

Solve

3^{x} = 1 : x = 0

x = 1, x = 0

3^{x} = 3^{6}

x, 3^{x} + 3^{y} = 10

2^{x} = 5

2^{x} = 1

2^{x} = 0