What is the answer to 2ln(1/(1-x))=a ?

The answer to 2ln(1/(1-x))=a is x=-(1-e^{a/2})/(e^{a/2)}

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2ln(1/(1-x))=a

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

x = - \frac{1 - e ^{\frac{a}{2}}}{e ^{\frac{a}{2}}}

Solution steps

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

Divide both sides by

2

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

Apply log rules

\frac{1}{1 - x} = e^{\frac{a}{2}}

Multiply both sides by

1 - x

\frac{1}{1 - x} (1 - x) = e^{\frac{a}{2}} (1 - x)

Simplify

1 = e^{\frac{a}{2}} (1 - x)

Solve

1 = e^{\frac{a}{2}} (1 - x) : x = - \frac{1 - e ^{\frac{a}{2}}}{e ^{\frac{a}{2}}}

x = - \frac{1 - e ^{\frac{a}{2}}}{e ^{\frac{a}{2}}}

Verify Solutions:

x = - \frac{1 - e ^{\frac{a}{2}}}{e ^{\frac{a}{2}}}

True

The solution is

x = - \frac{1 - e ^{\frac{a}{2}}}{e ^{\frac{a}{2}}}

lo g_{x} (\frac{81}{16}) = - 4

lo g_{6} (x + 4) + lo g_{6} (x + 3) = 1

2 lo g_{2} (x) = 3 + lo g_{2} (x + 1)

lo g_{x} (\frac{1}{81}) = - 4

y, x = lo g_{2} (y)

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