What is the answer to (2^x+1)/(2^x-1)=-6 ?

The answer to (2^x+1)/(2^x-1)=-6 is x=(ln(5/7))/(ln(2))

Solve for x: (2^x+1)/(2^x-1)=-6

The solution is x=(ln(5/7))/(ln(2))

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\frac{2 ^{x} + 1}{2 ^{x} - 1} = - 6

x = \frac{ln ( \frac{5}{7} )}{ln ( 2 )}

Decimal Notation

x = - 0.48542 \dots

Solution steps

\frac{2 ^{x} + 1}{2 ^{x} - 1} = - 6

Multiply both sides by

2^{x} - 1

\frac{2 ^{x} + 1}{2 ^{x} - 1} (2^{x} - 1) = - 6 (2^{x} - 1)

Simplify

2^{x} + 1 = - 6 (2^{x} - 1)

Expand

- 6 (2^{x} - 1) : - 6 \cdot 2^{x} + 6

2^{x} + 1 = - 6 \cdot 2^{x} + 6

Move

1

to the right side

2^{x} = - 6 \cdot 2^{x} + 5

Move

6 \cdot 2^{x}

to the left side

7 \cdot 2^{x} = 5

Divide both sides by

7

2^{x} = \frac{5}{7}

Apply exponent rules

x ln (2) = ln (\frac{5}{7})

Solve

x ln (2) = ln (\frac{5}{7}) : x = \frac{ln ( \frac{5}{7} )}{ln ( 2 )}

x = \frac{ln ( \frac{5}{7} )}{ln ( 2 )}

Verify Solutions:

x = \frac{ln ( \frac{5}{7} )}{ln ( 2 )}

True

The solution is

x = \frac{ln ( \frac{5}{7} )}{ln ( 2 )}

\frac{11}{1 + e ^{- x}} = 3

\frac{11}{1 + e ^{- x}} = 4

\frac{1}{4 ^{- x}} = \frac{1}{2}

8^{x + 2} = 32

343 = 7 2^{x + 2}

What is the answer to (2^x+1)/(2^x-1)=-6 ?
The answer to (2^x+1)/(2^x-1)=-6 is x=(ln(5/7))/(ln(2))
Solve for x: (2^x+1)/(2^x-1)=-6
The solution is x=(ln(5/7))/(ln(2))