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Popular >

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

Solution

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

Solution

x = ln (\frac{- 1 + 5}{2})

+1

Decimal Notation

x = - 0.48121 \dots

Solution steps

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

Apply exponent rules

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

Rewrite the equation with

e^{x} = u

(u)^{2} + u = 1

Solve

u^{2} + u = 1 : u = \frac{- 1 + 5}{2}, u = \frac{- 1 - 5}{2}

u = \frac{- 1 + 5}{2}, u = \frac{- 1 - 5}{2}

Substitute back

u = e^{x},

solve for

x

Solve

e^{x} = \frac{- 1 + 5}{2} : x = ln (\frac{- 1 + 5}{2})

Solve

e^{x} = \frac{- 1 - 5}{2} :

No Solution for

x \in R

x = ln (\frac{- 1 + 5}{2})

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123456789 = 3.5 (0.9825)^{x}

solvefor y,(5^{-1})^3=x^y solve for

y, (5^{- 1})^{3} = x^{y}

4 + 5 e^{x + 2} = 11

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Frequently Asked Questions (FAQ)

What is the answer to e^{2x}+e^x=1 ?
The answer to e^{2x}+e^x=1 is x=ln((-1+sqrt(5))/2)