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Popular >

1/(1-e^x)=5

Solution

\frac{1}{1 - e ^{x}} = 5

Solution

x = ln (\frac{4}{5})

+1

Decimal Notation

x = - 0.22314 \dots

Solution steps

\frac{1}{1 - e ^{x}} = 5

Multiply both sides by

1 - e^{x}

\frac{1}{1 - e ^{x}} (1 - e^{x}) = 5 (1 - e^{x})

Simplify

1 = 5 (1 - e^{x})

Switch sides

5 (1 - e^{x}) = 1

Divide both sides by

5

1 - e^{x} = \frac{1}{5}

Move

1

to the right side

- e^{x} = - \frac{4}{5}

Divide both sides by

- 1

e^{x} = \frac{4}{5}

Apply exponent rules

x = ln (\frac{4}{5})

Verify Solutions:

x = ln (\frac{4}{5})

True

The solution is

x = ln (\frac{4}{5})

Popular Examples

16 \cdot 1 0^{5 x} = 96

5^{x + 1} = 7

5^{x} - 0. 2^{x} = 4.8

2 e^{2 x} = 97

70 = 140 e^{30 x}

Frequently Asked Questions (FAQ)

What is the answer to 1/(1-e^x)=5 ?
The answer to 1/(1-e^x)=5 is x=ln(4/5)