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Popular >

e^x-2e^{-x}=1

Solution

e^{x} - 2 e^{- x} = 1

Solution

x = ln (2)

+1

Solution steps

e^{x} - 2 e^{- x} = 1

Apply exponent rules

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

Rewrite the equation with

e^{x} = u

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

Solve

u - 2 u^{- 1} = 1 : u = 2, u = - 1

u = 2, u = - 1

Substitute back

u = e^{x},

solve for

x

Solve

e^{x} = 2 : x = ln (2)

Solve

e^{x} = - 1 :

No Solution for

x \in R

x = ln (2)

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Frequently Asked Questions (FAQ)

What is the answer to e^x-2e^{-x}=1 ?
The answer to e^x-2e^{-x}=1 is x=ln(2)