What is the answer to log_{10}((x+1)/(x-1))=1 ?

The answer to log_{10}((x+1)/(x-1))=1 is x= 11/9

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log_{10}((x+1)/(x-1))=1

lo g_{10} (\frac{x + 1}{x - 1}) = 1

x = \frac{11}{9}

Solution steps

lo g_{10} (\frac{x + 1}{x - 1}) = 1

Apply log rules

\frac{x + 1}{x - 1} = 1 0^{1}

Multiply both sides by

x - 1

\frac{x + 1}{x - 1} (x - 1) = 1 0^{1} (x - 1)

Simplify

x + 1 = 10 (x - 1)

Solve

x + 1 = 10 (x - 1) : x = \frac{11}{9}

x = \frac{11}{9}

Verify Solutions:

x = \frac{11}{9}

True

The solution is

x = \frac{11}{9}

lo g_{10} (12) = lo g_{10} (x)

lo g_{10} (x) = 7.12735

10 - 4 ln (- 8 x) = 6

ln (x - 7) + ln (x + 2) = 0

lo g_{2} (2 x - 3) = 3

What is the answer to log_{10}((x+1)/(x-1))=1 ?
The answer to log_{10}((x+1)/(x-1))=1 is x= 11/9
Solve for x: log_{10}((x+1)/(x-1))=1
The solution is x= 11/9