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Popular >

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

Solution

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

Solution

x = ln (2)

+1

Decimal Notation

x = 0.69314 \dots

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)

Popular Examples

7^{x/2}=5^{1-x}

7^{\frac{x}{2}} = 5^{1 - x}

6e^{-4k-10}-4=63

6 e^{- 4 k - 10} - 4 = 63

e^{x} - 1 = 0

25^x+5^{3-2x}=30

2 5^{x} + 5^{3 - 2 x} = 30

3 (2^{x}) = 42

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)