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Popular >

e^x-12e^{-x}-1=0

Solution

e^{x} - 12 e^{- x} - 1 = 0

Solution

x = 2 ln (2)

+1

Decimal Notation

x = 1.38629 \dots

Solution steps

e^{x} - 12 e^{- x} - 1 = 0

Apply exponent rules

e^{x} - 12 (e^{x})^{- 1} - 1 = 0

Rewrite the equation with

e^{x} = u

u - 12 (u)^{- 1} - 1 = 0

Solve

u - 12 u^{- 1} - 1 = 0 : u = 4, u = - 3

u = 4, u = - 3

Substitute back

u = e^{x},

solve for

x

Solve

e^{x} = 4 : x = 2 ln (2)

Solve

e^{x} = - 3 :

No Solution for

x \in R

x = 2 ln (2)

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\frac{( 4 \cdot 1 0 ^{- 38} )}{27}

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Frequently Asked Questions (FAQ)

What is the answer to e^x-12e^{-x}-1=0 ?
The answer to e^x-12e^{-x}-1=0 is x=2ln(2)