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Popular >

e^{-2t}-4*e^{-t}+4=0

Solution

e^{- 2 t} - 4 \cdot e^{- t} + 4 = 0

Solution

t = - ln (2)

+1

Decimal Notation

t = - 0.69314 \dots

Solution steps

e^{- 2 t} - 4 e^{- t} + 4 = 0

Apply exponent rules

(e^{t})^{- 2} - 4 (e^{t})^{- 1} + 4 = 0

Rewrite the equation with

e^{t} = u

(u)^{- 2} - 4 (u)^{- 1} + 4 = 0

Solve

u^{- 2} - 4 u^{- 1} + 4 = 0 : u = \frac{1}{2}

u = \frac{1}{2}

Substitute back

u = e^{t},

solve for

t

Solve

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

t = - ln (2)

Popular Examples

4^{- 3 v} = 64

3^{2x+1}+3^x-2=0

3^{2 x + 1} + 3^{x} - 2 = 0

2^{- 3 x} = 16

e^{y} + y = 1

(e^{1/x})/(x^2)=0

\frac{e ^{\frac{1}{x}}}{x ^{2}} = 0

Frequently Asked Questions (FAQ)

What is the answer to e^{-2t}-4*e^{-t}+4=0 ?
The answer to e^{-2t}-4*e^{-t}+4=0 is t=-ln(2)