What is the answer to 3^x+3^{-x}=5 ?

The answer to 3^x+3^{-x}=5 is x=(ln((5+sqrt(21))/2))/(ln(3)),x=(ln((5-sqrt(21))/2))/(ln(3))

Solve for x: 3^x+3^{-x}=5

The solution is x=(ln((5+sqrt(21))/2))/(ln(3)),x=(ln((5-sqrt(21))/2))/(ln(3))

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

x = \frac{ln ( \frac{5 + 21}{2} )}{ln ( 3 )}, x = \frac{ln ( \frac{5 - 21}{2} )}{ln ( 3 )}

Decimal Notation

x = 1.42616 \dots, x = - 1.42616 \dots

Solution steps

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

Apply exponent rules

3^{x} + (3^{x})^{- 1} = 5

Rewrite the equation with

3^{x} = u

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

Solve

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

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

Substitute back

u = 3^{x},

solve for

x

Solve

3^{x} = \frac{5 + 21}{2} : x = \frac{ln ( \frac{5 + 21}{2} )}{ln ( 3 )}

Solve

3^{x} = \frac{5 - 21}{2} : x = \frac{ln ( \frac{5 - 21}{2} )}{ln ( 3 )}

x = \frac{ln ( \frac{5 + 21}{2} )}{ln ( 3 )}, x = \frac{ln ( \frac{5 - 21}{2} )}{ln ( 3 )}

ln (e^{x} - 3 e^{- x}) = ln (2)

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

3^{2 x - 1} = 7^{x}

(7^{x})^{x - 3} = 1

e^{30 k} = \frac{1}{2}

What is the answer to 3^x+3^{-x}=5 ?
The answer to 3^x+3^{-x}=5 is x=(ln((5+sqrt(21))/2))/(ln(3)),x=(ln((5-sqrt(21))/2))/(ln(3))
Solve for x: 3^x+3^{-x}=5
The solution is x=(ln((5+sqrt(21))/2))/(ln(3)),x=(ln((5-sqrt(21))/2))/(ln(3))