What is the answer to e^x+2e^{-x}=80 ?

The answer to e^x+2e^{-x}=80 is x=ln(40+sqrt(1598)),x=ln(40-sqrt(1598))

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e^x+2e^{-x}=80

e^{x} + 2 e^{- x} = 80

x = ln (40 + 1598), x = ln (40 - 1598)

Decimal Notation

x = 4.38171 \dots, x = - 3.68856 \dots

Solution steps

e^{x} + 2 e^{- x} = 80

Apply exponent rules

e^{x} + 2 (e^{x})^{- 1} = 80

Rewrite the equation with

e^{x} = u

u + 2 (u)^{- 1} = 80

Solve

u + 2 u^{- 1} = 80 : u = 40 + 1598, u = 40 - 1598

u = 40 + 1598, u = 40 - 1598

Substitute back

u = e^{x},

solve for

x

Solve

e^{x} = 40 + 1598 : x = ln (40 + 1598)

Solve

e^{x} = 40 - 1598 : x = ln (40 - 1598)

x = ln (40 + 1598), x = ln (40 - 1598)

27 = (\frac{1}{3})^{\frac{x}{2}}

8^{7} = 8^{3} \cdot 8^{x}

2 5^{x + 2} = 12 5^{x^{2} + 1}

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

4 ln (e^{x}) = 26

What is the answer to e^x+2e^{-x}=80 ?
The answer to e^x+2e^{-x}=80 is x=ln(40+sqrt(1598)),x=ln(40-sqrt(1598))