What is the answer to (2^x)/(1-2^x)=3 ?

The answer to (2^x)/(1-2^x)=3 is x=(ln(3/4))/(ln(2))

Solve for x: (2^x)/(1-2^x)=3

The solution is x=(ln(3/4))/(ln(2))

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

x = \frac{ln ( \frac{3}{4} )}{ln ( 2 )}

Decimal Notation

x = - 0.41503 \dots

Solution steps

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

Multiply both sides by

1 - 2^{x}

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

Simplify

2^{x} = 3 (1 - 2^{x})

Expand

3 (1 - 2^{x}) : 3 - 3 \cdot 2^{x}

2^{x} = 3 - 3 \cdot 2^{x}

Move

3 \cdot 2^{x}

to the left side

4 \cdot 2^{x} = 3

Divide both sides by

4

2^{x} = \frac{3}{4}

Apply exponent rules

x ln (2) = ln (\frac{3}{4})

Solve

x ln (2) = ln (\frac{3}{4}) : x = \frac{ln ( \frac{3}{4} )}{ln ( 2 )}

x = \frac{ln ( \frac{3}{4} )}{ln ( 2 )}

Verify Solutions:

x = \frac{ln ( \frac{3}{4} )}{ln ( 2 )}

True

The solution is

x = \frac{ln ( \frac{3}{4} )}{ln ( 2 )}

4 (\frac{2}{3})^{x^{2} - 5 x + 4} = 9

e^{k x} = 0

2^{x - 1} + \frac{1}{2 ^{x - 3}} = 5

7 \cdot e^{0.1 t} = 47

e^{7 - 4 x} = 5

What is the answer to (2^x)/(1-2^x)=3 ?
The answer to (2^x)/(1-2^x)=3 is x=(ln(3/4))/(ln(2))
Solve for x: (2^x)/(1-2^x)=3
The solution is x=(ln(3/4))/(ln(2))