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

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

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

The solution is x=(1+sqrt(1+4e))/2

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

x = \frac{1 + 1 + 4 e}{2}

Decimal Notation

x = 2.22287 \dots

Solution steps

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

Apply log rules

x (x - 1) = e

Solve

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

x = \frac{1 + 1 + 4 e}{2}, x = \frac{1 - 1 + 4 e}{2}

Verify Solutions:

x = \frac{1 + 1 + 4 e}{2}

True

, x = \frac{1 - 1 + 4 e}{2}

False

The solution is

x = \frac{1 + 1 + 4 e}{2}

lo g_{3} (2 x + 3) - lo g_{3} (x + 2) = 4

ln (x^{2} - 3) = 4

lo g_{17} (x^{3} + 2 x^{2} - x + 15) = 1

lo g_{4} (22 - 4 x) = 2

lo g_{2} (x^{5}) = lo g_{10} (2 x)^{4}

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