What is the answer to ln(x/(x-1))=1 ?

The answer to ln(x/(x-1))=1 is x= e/(e-1)

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ln(x/(x-1))=1

ln (\frac{x}{x - 1}) = 1

x = \frac{e}{e - 1}

Decimal

x = 1.58197 \dots

Solution steps

ln (\frac{x}{x - 1}) = 1

Apply log rules

\frac{x}{x - 1} = e^{1}

Multiply both sides by

x - 1

\frac{x}{x - 1} (x - 1) = e^{1} (x - 1)

Simplify

x = e (x - 1)

Solve

x = e (x - 1) : x = \frac{e}{e - 1}

x = \frac{e}{e - 1}

Verify Solutions:

x = \frac{e}{e - 1}

True

The solution is

x = \frac{e}{e - 1}

10 = 10 lo g_{10} (x)

ln (y) = 0.66

2 lo g_{5} (x) = - lo g_{5} (25)

x, ln (x) = y + 2

lo g_{8} (\frac{x + 5}{x - 2}) = 1