What is the answer to ln(x)+ln(x-2)=-1 ?

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

Solve for x: ln(x)+ln(x-2)=-1

The solution is x=(2e+sqrt(4e^2+4e))/(2e)

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ln (x) + ln (x - 2) = - 1

x = \frac{2 e + 4 e ^{2} + 4 e}{2 e}

Decimal Notation

x = 2.16956 \dots

Solution steps

ln (x) + ln (x - 2) = - 1

Apply log rules

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

Solve

x (x - 2) = \frac{1}{e} : x = \frac{2 e + 4 e ^{2} + 4 e}{2 e}, x = \frac{2 e - 4 e ^{2} + 4 e}{2 e}

x = \frac{2 e + 4 e ^{2} + 4 e}{2 e}, x = \frac{2 e - 4 e ^{2} + 4 e}{2 e}

Verify Solutions:

x = \frac{2 e + 4 e ^{2} + 4 e}{2 e}

True

, x = \frac{2 e - 4 e ^{2} + 4 e}{2 e}

False

The solution is

x = \frac{2 e + 4 e ^{2} + 4 e}{2 e}

lo g_{3} (x) = 1 + lo g_{3} (x - 6)

9 = lo g_{2} (2 x)

lo g_{10} (x + 2) = 1

x, ln (x^{2} - 2 x y) = c

y, x = 3 lo g_{y} (2)

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