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

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

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

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

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

Decimal

c = 0.62122 \dots

Solution steps

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

Divide both sides by

- 4

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

Simplify

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

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

Apply exponent rules

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

Solve

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

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

9^{x} - 3^{x + 1} = 54

1 9^{x} = 2

5 \cdot 2^{x + 1} = 15

3 \times 2^{x} - 2^{x} = 1

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

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