What is the answer to 2^x+2^{-x}=10 ?

The answer to 2^x+2^{-x}=10 is x=(ln(5+2sqrt(6)))/(ln(2)),x=(ln(5-2sqrt(6)))/(ln(2))

Solve for x: 2^x+2^{-x}=10

The solution is x=(ln(5+2sqrt(6)))/(ln(2)),x=(ln(5-2sqrt(6)))/(ln(2))

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2^{x} + 2^{- x} = 10

x = \frac{ln ( 5 + 2 6 )}{ln ( 2 )}, x = \frac{ln ( 5 - 2 6 )}{ln ( 2 )}

Decimal Notation

x = 3.30727 \dots, x = - 3.30727 \dots

Solution steps

2^{x} + 2^{- x} = 10

Apply exponent rules

2^{x} + (2^{x})^{- 1} = 10

Rewrite the equation with

2^{x} = u

u + (u)^{- 1} = 10

Solve

u + u^{- 1} = 10 : u = 5 + 26, u = 5 - 26

u = 5 + 26, u = 5 - 26

Substitute back

u = 2^{x},

solve for

x

Solve

2^{x} = 5 + 26 : x = \frac{ln ( 5 + 2 6 )}{ln ( 2 )}

Solve

2^{x} = 5 - 26 : x = \frac{ln ( 5 - 2 6 )}{ln ( 2 )}

x = \frac{ln ( 5 + 2 6 )}{ln ( 2 )}, x = \frac{ln ( 5 - 2 6 )}{ln ( 2 )}

4^{2 x - 1} = 8^{x - 3}

\frac{2 ^{x}}{2 ^{x}} = 2^{- 2 x}

8 1^{5} = 3^{x}

3^{2 x} - 3^{x + 1} + 2 = 0

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

What is the answer to 2^x+2^{-x}=10 ?
The answer to 2^x+2^{-x}=10 is x=(ln(5+2sqrt(6)))/(ln(2)),x=(ln(5-2sqrt(6)))/(ln(2))
Solve for x: 2^x+2^{-x}=10
The solution is x=(ln(5+2sqrt(6)))/(ln(2)),x=(ln(5-2sqrt(6)))/(ln(2))