What is the answer to 2^{(-x)}+2^x=5 ?

The answer to 2^{(-x)}+2^x=5 is x=(ln((5+sqrt(21))/2))/(ln(2)),x=(ln((5-sqrt(21))/2))/(ln(2))

Solve for x: 2^{(-x)}+2^x=5

The solution is x=(ln((5+sqrt(21))/2))/(ln(2)),x=(ln((5-sqrt(21))/2))/(ln(2))

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2^{(- x)} + 2^{x} = 5

x = \frac{ln ( \frac{5 + 21}{2} )}{ln ( 2 )}, x = \frac{ln ( \frac{5 - 21}{2} )}{ln ( 2 )}

Decimal Notation

x = 2.26041 \dots, x = - 2.26041 \dots

Solution steps

2^{(- x)} + 2^{x} = 5

Apply exponent rules

(2^{x})^{- 1} + 2^{x} = 5

Rewrite the equation with

2^{x} = u

(u)^{- 1} + u = 5

Solve

u^{- 1} + u = 5 : u = \frac{5 + 21}{2}, u = \frac{5 - 21}{2}

u = \frac{5 + 21}{2}, u = \frac{5 - 21}{2}

Substitute back

u = 2^{x},

solve for

x

Solve

2^{x} = \frac{5 + 21}{2} : x = \frac{ln ( \frac{5 + 21}{2} )}{ln ( 2 )}

Solve

2^{x} = \frac{5 - 21}{2} : x = \frac{ln ( \frac{5 - 21}{2} )}{ln ( 2 )}

x = \frac{ln ( \frac{5 + 21}{2} )}{ln ( 2 )}, x = \frac{ln ( \frac{5 - 21}{2} )}{ln ( 2 )}

3^{2 x} + 3^{x} = 56

50000 = 100 \cdot 2^{\frac{t}{3}}

12 8^{9} = 2^{x}

1 0^{4 x - 6} = 9^{8 x - 9}

7^{x - 2} = 1

What is the answer to 2^{(-x)}+2^x=5 ?
The answer to 2^{(-x)}+2^x=5 is x=(ln((5+sqrt(21))/2))/(ln(2)),x=(ln((5-sqrt(21))/2))/(ln(2))
Solve for x: 2^{(-x)}+2^x=5
The solution is x=(ln((5+sqrt(21))/2))/(ln(2)),x=(ln((5-sqrt(21))/2))/(ln(2))