What is the answer to 2^x+2^{-x}=4 ?

The answer to 2^x+2^{-x}=4 is x=(ln(2+sqrt(3)))/(ln(2)),x=(ln(2-sqrt(3)))/(ln(2))

Solve for x: 2^x+2^{-x}=4

The solution is x=(ln(2+sqrt(3)))/(ln(2)),x=(ln(2-sqrt(3)))/(ln(2))

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

x = \frac{ln ( 2 + 3 )}{ln ( 2 )}, x = \frac{ln ( 2 - 3 )}{ln ( 2 )}

Decimal Notation

x = 1.89996 \dots, x = - 1.89996 \dots

Solution steps

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

Apply exponent rules

2^{x} + (2^{x})^{- 1} = 4

Rewrite the equation with

2^{x} = u

u + (u)^{- 1} = 4

Solve

u + u^{- 1} = 4 : u = 2 + 3, u = 2 - 3

u = 2 + 3, u = 2 - 3

Substitute back

u = 2^{x},

solve for

x

Solve

2^{x} = 2 + 3 : x = \frac{ln ( 2 + 3 )}{ln ( 2 )}

Solve

2^{x} = 2 - 3 : x = \frac{ln ( 2 - 3 )}{ln ( 2 )}

x = \frac{ln ( 2 + 3 )}{ln ( 2 )}, x = \frac{ln ( 2 - 3 )}{ln ( 2 )}

(- 3^{3})^{x} = - 3

lo g_{2} (8^{x}) = - 3

x, 3^{x} = 243

3 e^{x} = 5 + 8 e^{- x}

3 (1 0^{x + 4} - 3) = 9

What is the answer to 2^x+2^{-x}=4 ?
The answer to 2^x+2^{-x}=4 is x=(ln(2+sqrt(3)))/(ln(2)),x=(ln(2-sqrt(3)))/(ln(2))
Solve for x: 2^x+2^{-x}=4
The solution is x=(ln(2+sqrt(3)))/(ln(2)),x=(ln(2-sqrt(3)))/(ln(2))