What is the answer to ln((x^2-4)/(x-1))=0 ?

The answer to ln((x^2-4)/(x-1))=0 is x=(1+sqrt(13))/2 ,x=(1-sqrt(13))/2

Solve for x: ln((x^2-4)/(x-1))=0

The solution is x=(1+sqrt(13))/2 ,x=(1-sqrt(13))/2

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ln (\frac{x ^{2} - 4}{x - 1}) = 0

x = \frac{1 + 13}{2}, x = \frac{1 - 13}{2}

Decimal Notation

x = 2.30277 \dots, x = - 1.30277 \dots

Solution steps

ln (\frac{x ^{2} - 4}{x - 1}) = 0

Apply log rules

\frac{x ^{2} - 4}{x - 1} = e^{0}

Multiply both sides by

x - 1

\frac{x ^{2} - 4}{x - 1} (x - 1) = e^{0} (x - 1)

Simplify

x^{2} - 4 = x - 1

Solve

x^{2} - 4 = x - 1 : x = \frac{1 + 13}{2}, x = \frac{1 - 13}{2}

x = \frac{1 + 13}{2}, x = \frac{1 - 13}{2}

Verify Solutions:

x = \frac{1 + 13}{2}

True

, x = \frac{1 - 13}{2}

True

The solutions are

x = \frac{1 + 13}{2}, x = \frac{1 - 13}{2}

lo g_{2} ((2 x + 14)^{3}) = 18

lo g_{3} (lo g_{2} (x + 12)) = 2

- 10.216 = ln (10 x)

ln (2 x + 3) + ln (3 x) = 2

lo g_{4} (3 x + 4) + lo g_{4} (16) = 1

What is the answer to ln((x^2-4)/(x-1))=0 ?
The answer to ln((x^2-4)/(x-1))=0 is x=(1+sqrt(13))/2 ,x=(1-sqrt(13))/2
Solve for x: ln((x^2-4)/(x-1))=0
The solution is x=(1+sqrt(13))/2 ,x=(1-sqrt(13))/2