What is the answer to log_{2}(((x+1))/(x-1))=3 ?

The answer to log_{2}(((x+1))/(x-1))=3 is x= 9/7

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log_{2}(((x+1))/(x-1))=3

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

x = \frac{9}{7}

Decimal Notation

x = 1.28571 \dots

Solution steps

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

Apply log rules

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

Multiply both sides by

x - 1

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

Simplify

x + 1 = 8 (x - 1)

Solve

x + 1 = 8 (x - 1) : x = \frac{9}{7}

x = \frac{9}{7}

Verify Solutions:

x = \frac{9}{7}

True

The solution is

x = \frac{9}{7}

(t) = 3 lo g_{2} (- 3 + t)

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

20 lo g_{10} (\frac{1}{k}) = 17.1

y, ln (y) = - 2 t

lo g_{10} (x) = - 1.187087

What is the answer to log_{2}(((x+1))/(x-1))=3 ?
The answer to log_{2}(((x+1))/(x-1))=3 is x= 9/7
Solve for x: log_{2}(((x+1))/(x-1))=3
The solution is x= 9/7