What is the answer to 2^x+2^{2-x}=17 ?

The answer to 2^x+2^{2-x}=17 is x=(ln((17+sqrt(273))/2))/(ln(2)),x=(ln((17-sqrt(273))/2))/(ln(2))

Solve for x: 2^x+2^{2-x}=17

The solution is x=(ln((17+sqrt(273))/2))/(ln(2)),x=(ln((17-sqrt(273))/2))/(ln(2))

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2^{x} + 2^{2 - x} = 17

x = \frac{ln ( \frac{17 + 273}{2} )}{ln ( 2 )}, x = \frac{ln ( \frac{17 - 273}{2} )}{ln ( 2 )}

Decimal Notation

x = 4.06706 \dots, x = - 2.06706 \dots

Solution steps

2^{x} + 2^{2 - x} = 17

Apply exponent rules

2^{x} + (2^{x})^{- 1} \cdot 2^{2} = 17

Rewrite the equation with

2^{x} = u

u + (u)^{- 1} \cdot 2^{2} = 17

Solve

u + u^{- 1} \cdot 2^{2} = 17 : u = \frac{17 + 273}{2}, u = \frac{17 - 273}{2}

u = \frac{17 + 273}{2}, u = \frac{17 - 273}{2}

Substitute back

u = 2^{x},

solve for

x

Solve

2^{x} = \frac{17 + 273}{2} : x = \frac{ln ( \frac{17 + 273}{2} )}{ln ( 2 )}

Solve

2^{x} = \frac{17 - 273}{2} : x = \frac{ln ( \frac{17 - 273}{2} )}{ln ( 2 )}

x = \frac{ln ( \frac{17 + 273}{2} )}{ln ( 2 )}, x = \frac{ln ( \frac{17 - 273}{2} )}{ln ( 2 )}

8^{- 1} \cdot 2^{(2 x + 1)} = 64

6^{x - 3} = 2^{x}

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

7^{- 2 x - 4} = 49

- 50 (1 - 2^{x}) = 123723

What is the answer to 2^x+2^{2-x}=17 ?
The answer to 2^x+2^{2-x}=17 is x=(ln((17+sqrt(273))/2))/(ln(2)),x=(ln((17-sqrt(273))/2))/(ln(2))
Solve for x: 2^x+2^{2-x}=17
The solution is x=(ln((17+sqrt(273))/2))/(ln(2)),x=(ln((17-sqrt(273))/2))/(ln(2))