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

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

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

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

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

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

Decimal

x = 3.26388 \dots

Solution steps

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

Apply log rules

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

Solve

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

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

Verify Solutions:

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

True

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

False

The solution is

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

lo g_{2} (5 x + 6) = 3

lo g_{10} (x + 13) = lo g_{10} (x) + lo g_{10} (13)

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

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

lo g_{1 + x} (\frac{400}{13}) = 20

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