What is the answer to ln((x-5)/(x-1))=ln(6) ?

The answer to ln((x-5)/(x-1))=ln(6) is x= 1/5

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ln((x-5)/(x-1))=ln(6)

ln (\frac{x - 5}{x - 1}) = ln (6)

x = \frac{1}{5}

Decimal Notation

x = 0.2

Solution steps

ln (\frac{x - 5}{x - 1}) = ln (6)

Apply log rules

\frac{x - 5}{x - 1} = 6

Multiply both sides by

x - 1

\frac{x - 5}{x - 1} (x - 1) = 6 (x - 1)

Simplify

x - 5 = 6 (x - 1)

Solve

x - 5 = 6 (x - 1) : x = \frac{1}{5}

x = \frac{1}{5}

Verify Solutions:

x = \frac{1}{5}

True

The solution is

x = \frac{1}{5}

0.27 = ln (x)

2 ln (x) = 3

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

lo g_{10} (x) = lo g_{10} (2)

ln (y) = 14

What is the answer to ln((x-5)/(x-1))=ln(6) ?
The answer to ln((x-5)/(x-1))=ln(6) is x= 1/5
Solve for x: ln((x-5)/(x-1))=ln(6)
The solution is x= 1/5