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

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

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

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

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

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

Decimal Notation

x = 4.49585 \dots

Solution steps

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

Apply log rules

(x - 1)^{2} = e x

Solve

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

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

Verify Solutions:

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

True

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

False

The solution is

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

x, lo g_{e} (2 x - 1) = - 3

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

1.5 n^{2} - 7.5 n lo g_{10} (n) = 0

6 ln (5 x - 3) + 12 = 0

(1 - ln (x)) d x = 0

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