What is the answer to 3^x+3^{2-x}=11 ?

The answer to 3^x+3^{2-x}=11 is x=(ln((11+sqrt(85))/2))/(ln(3)),x=(ln((11-sqrt(85))/2))/(ln(3))

Solve for x: 3^x+3^{2-x}=11

The solution is x=(ln((11+sqrt(85))/2))/(ln(3)),x=(ln((11-sqrt(85))/2))/(ln(3))

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3^{x} + 3^{2 - x} = 11

x = \frac{ln ( \frac{11 + 85}{2} )}{ln ( 3 )}, x = \frac{ln ( \frac{11 - 85}{2} )}{ln ( 3 )}

Decimal Notation

x = 2.10584 \dots, x = - 0.10584 \dots

Solution steps

3^{x} + 3^{2 - x} = 11

Apply exponent rules

3^{x} + (3^{x})^{- 1} \cdot 3^{2} = 11

Rewrite the equation with

3^{x} = u

u + (u)^{- 1} \cdot 3^{2} = 11

Solve

u + u^{- 1} \cdot 3^{2} = 11 : u = \frac{11 + 85}{2}, u = \frac{11 - 85}{2}

u = \frac{11 + 85}{2}, u = \frac{11 - 85}{2}

Substitute back

u = 3^{x},

solve for

x

Solve

3^{x} = \frac{11 + 85}{2} : x = \frac{ln ( \frac{11 + 85}{2} )}{ln ( 3 )}

Solve

3^{x} = \frac{11 - 85}{2} : x = \frac{ln ( \frac{11 - 85}{2} )}{ln ( 3 )}

x = \frac{ln ( \frac{11 + 85}{2} )}{ln ( 3 )}, x = \frac{ln ( \frac{11 - 85}{2} )}{ln ( 3 )}

25 6^{b + 2} = 4^{2 - 2 b}

lo g_{a} (a^{x}) = x

1 6^{x} - 4^{x + 1} + 3 = 0

625 = 5^{6 - 2 x}

2400 = 7500 (10)^{- x}

What is the answer to 3^x+3^{2-x}=11 ?
The answer to 3^x+3^{2-x}=11 is x=(ln((11+sqrt(85))/2))/(ln(3)),x=(ln((11-sqrt(85))/2))/(ln(3))
Solve for x: 3^x+3^{2-x}=11
The solution is x=(ln((11+sqrt(85))/2))/(ln(3)),x=(ln((11-sqrt(85))/2))/(ln(3))