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Popular >

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

Solution

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

Solution

x = ln (1 + 2)

+1

Decimal Notation

x = 0.88137 \dots

Solution steps

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

Apply exponent rules

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

Rewrite the equation with

e^{x} = u

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

Solve

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

u = 1 + 2, u = 1 - 2

Substitute back

u = e^{x},

solve for

x

Solve

e^{x} = 1 + 2 : x = ln (1 + 2)

Solve

e^{x} = 1 - 2 :

No Solution for

x \in R

x = ln (1 + 2)

Popular Examples

9^{x} = 2 7^{(x + 6)}

9^{3 x + 1} = 6

2e^{-x}-e^x+1=0

2 e^{- x} - e^{x} + 1 = 0

2^x-2^{x+2}=-12

2^{x} - 2^{x + 2} = - 12

3^{3 x - 2} = 15

Frequently Asked Questions (FAQ)

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