What is the answer to -4e^{-4x}=(e^{-12}-1)/3 ?

The answer to -4e^{-4x}=(e^{-12}-1)/3 is x=-(ln((e^{12}-1)/(12e^{12)}))/4

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-4e^{-4x}=(e^{-12}-1)/3

- 4 e^{- 4 x} = \frac{e ^{- 12} - 1}{3}

x = - \frac{ln ( \frac{e ^{12} - 1}{12 e ^{12}} )}{4}

Decimal Notation

x = 0.62122 \dots

Solution steps

- 4 e^{- 4 x} = \frac{e ^{- 12} - 1}{3}

Divide both sides by

- 4

e^{- 4 x} = - \frac{e ^{- 12} - 1}{12}

Simplify

- \frac{e ^{- 12} - 1}{12} : - \frac{1 - e ^{12}}{12 e ^{12}}

e^{- 4 x} = - \frac{1 - e ^{12}}{12 e ^{12}}

Apply exponent rules

- 4 x = ln (- \frac{1 - e ^{12}}{12 e ^{12}})

Solve

- 4 x = ln (- \frac{1 - e ^{12}}{12 e ^{12}}) : x = - \frac{ln ( \frac{e ^{12} - 1}{12 e ^{12}} )}{4}

x = - \frac{ln ( \frac{e ^{12} - 1}{12 e ^{12}} )}{4}

5^{x - 4} = 25

5^{x} - \frac{1}{5 ^{x - 2}} = 24

1 0^{6 x} = 3^{3 x + 4}

6^{x} = 60

6^{x} = 18

What is the answer to -4e^{-4x}=(e^{-12}-1)/3 ?
The answer to -4e^{-4x}=(e^{-12}-1)/3 is x=-(ln((e^{12}-1)/(12e^{12)}))/4