What is the answer to log_{2}((x+1)/(x-1))=2 ?

The answer to log_{2}((x+1)/(x-1))=2 is x= 5/3

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log_{2}((x+1)/(x-1))=2

lo g_{2} (\frac{x + 1}{x - 1}) = 2

x = \frac{5}{3}

Decimal Notation

x = 1.66666 \dots

Solution steps

lo g_{2} (\frac{x + 1}{x - 1}) = 2

Apply log rules

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

Multiply both sides by

x - 1

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

Simplify

x + 1 = 4 (x - 1)

Solve

x + 1 = 4 (x - 1) : x = \frac{5}{3}

x = \frac{5}{3}

Verify Solutions:

x = \frac{5}{3}

True

The solution is

x = \frac{5}{3}

lo g_{10} (3 x) = lo g_{10} (9)

ln (x) = 0.95 x + 0.01

lo g_{10} (2 x) + lo g_{10} (x - 5) = 2

0 = lo g_{10} (10 + \frac{3 q}{2})

ln (3 x - 12) = 9

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