What is the answer to e^x+e^{-x}=6 ?

The answer to e^x+e^{-x}=6 is x=ln(3+2sqrt(2)),x=ln(3-2sqrt(2))

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e^x+e^{-x}=6

e^{x} + e^{- x} = 6

x = ln (3 + 22), x = ln (3 - 22)

Decimal Notation

x = 1.76274 \dots, x = - 1.76274 \dots

Solution steps

e^{x} + e^{- x} = 6

Apply exponent rules

e^{x} + (e^{x})^{- 1} = 6

Rewrite the equation with

e^{x} = u

u + (u)^{- 1} = 6

Solve

u + u^{- 1} = 6 : u = 3 + 22, u = 3 - 22

u = 3 + 22, u = 3 - 22

Substitute back

u = e^{x},

solve for

x

Solve

e^{x} = 3 + 22 : x = ln (3 + 22)

Solve

e^{x} = 3 - 22 : x = ln (3 - 22)

x = ln (3 + 22), x = ln (3 - 22)

2 = 4^{n}

2 e^{2 x} - 5 e^{x} - 3 = 0

9^{x} = e^{x + 8}

6^{2 x - 3} = 6^{- 2 x + 1}

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

What is the answer to e^x+e^{-x}=6 ?
The answer to e^x+e^{-x}=6 is x=ln(3+2sqrt(2)),x=ln(3-2sqrt(2))