What is the answer to e^{-6x}-6e^{-3x}=-8 ?

The answer to e^{-6x}-6e^{-3x}=-8 is x=-2/3 ln(2),x=-1/3 ln(2)

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e^{-6x}-6e^{-3x}=-8

e^{- 6 x} - 6 e^{- 3 x} = - 8

x = - \frac{2}{3} ln (2), x = - \frac{1}{3} ln (2)

Decimal Notation

x = - 0.46209 \dots, x = - 0.23104 \dots

Solution steps

e^{- 6 x} - 6 e^{- 3 x} = - 8

Apply exponent rules

(e^{x})^{- 6} - 6 (e^{x})^{- 3} = - 8

Rewrite the equation with

e^{x} = u

(u)^{- 6} - 6 (u)^{- 3} = - 8

Solve

Substitute back

u = e^{x},

solve for

x

Solve

x = - \frac{2}{3} ln (2), x = - \frac{1}{3} ln (2)

9^{x} = \frac{1}{9}

2^{5 x - 6} = 1 6^{5 x + 3}

e^{x^{x}} = 2

3^{x + 1} \cdot 2^{x + 1} = 36

3^{x + 1} = 10

What is the answer to e^{-6x}-6e^{-3x}=-8 ?
The answer to e^{-6x}-6e^{-3x}=-8 is x=-2/3 ln(2),x=-1/3 ln(2)