What is the answer to ((2^x+1))/((2^x-1))=5 ?

The answer to ((2^x+1))/((2^x-1))=5 is x=(ln(3/2))/(ln(2))

Solve for x: ((2^x+1))/((2^x-1))=5

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

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

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

Decimal Notation

x = 0.58496 \dots

Solution steps

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

Multiply both sides by

2^{x} - 1

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

Simplify

2^{x} + 1 = 5 (2^{x} - 1)

Expand

5 (2^{x} - 1) : 5 \cdot 2^{x} - 5

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

Move

1

to the right side

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

Move

5 \cdot 2^{x}

to the left side

- 4 \cdot 2^{x} = - 6

Divide both sides by

- 4

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

Apply exponent rules

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

Solve

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

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

Verify Solutions:

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

True

The solution is

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

\frac{( 7 ^{3 - 2 x} )}{( 7 ^{7 - 5 x} )} = 4 9^{3 x - 14}

(3^{4})^{x} = 5

1 = 3^{2 x}

\frac{e ^{- t \cdot 1000}}{41.3} = 1

9^{x} - 3^{x} - 72 = 0

What is the answer to ((2^x+1))/((2^x-1))=5 ?
The answer to ((2^x+1))/((2^x-1))=5 is x=(ln(3/2))/(ln(2))
Solve for x: ((2^x+1))/((2^x-1))=5
The solution is x=(ln(3/2))/(ln(2))