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Popular >

e^{-2x}-3e^{-x}=-2

Solution

e^{- 2 x} - 3 e^{- x} = - 2

Solution

x = - ln (2), x = 0

+1

Decimal Notation

x = - 0.69314 \dots, x = 0

Solution steps

e^{- 2 x} - 3 e^{- x} = - 2

Apply exponent rules

(e^{x})^{- 2} - 3 (e^{x})^{- 1} = - 2

Rewrite the equation with

e^{x} = u

(u)^{- 2} - 3 (u)^{- 1} = - 2

Solve

u^{- 2} - 3 u^{- 1} = - 2 : u = \frac{1}{2}, u = 1

u = \frac{1}{2}, u = 1

Substitute back

u = e^{x},

solve for

x

Solve

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

Solve

e^{x} = 1 : x = 0

x = - ln (2), x = 0

Popular Examples

100000=50000*(1+0.04)^n

100000 = 50000 \cdot (1 + 0.04)^{n}

10e^{6x}=5e^{-3x}

10 e^{6 x} = 5 e^{- 3 x}

8 1^{x} = 2 7^{- x}

\sqrt[y+12]{12}=12

3^{x^{2} - x} = 729

Frequently Asked Questions (FAQ)

What is the answer to e^{-2x}-3e^{-x}=-2 ?
The answer to e^{-2x}-3e^{-x}=-2 is x=-ln(2),x=0