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Popular >

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

Solution

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

Solution

x = ln (\frac{- 1 + 17}{2})

+1

Decimal Notation

x = 0.44568 \dots

Solution steps

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

Apply exponent rules

(e^{x})^{2} + e^{x} = 4

Rewrite the equation with

e^{x} = u

(u)^{2} + u = 4

Solve

u^{2} + u = 4 : u = \frac{- 1 + 17}{2}, u = \frac{- 1 - 17}{2}

u = \frac{- 1 + 17}{2}, u = \frac{- 1 - 17}{2}

Substitute back

u = e^{x},

solve for

x

Solve

e^{x} = \frac{- 1 + 17}{2} : x = ln (\frac{- 1 + 17}{2})

Solve

e^{x} = \frac{- 1 - 17}{2} :

No Solution for

x \in R

x = ln (\frac{- 1 + 17}{2})

Popular Examples

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3^{3x}=27^{2x+3}

3^{3 x} = 2 7^{2 x + 3}

25 e^{2 x} = 25

5^{\frac{x - 3}{4}} = 25

2 e^{6 x} = 18

Frequently Asked Questions (FAQ)

What is the answer to e^{2x}+e^x=4 ?
The answer to e^{2x}+e^x=4 is x=ln((-1+sqrt(17))/2)