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

The answer to ln^2(x-1)-2ln(x-1)=0 is x=e^2+1,x=2

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ln^2(x-1)-2ln(x-1)=0

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

x = e^{2} + 1, x = 2

Decimal Notation

x = 8.38905 \dots, x = 2

Solution steps

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

Rewrite the equation with

ln (x - 1) = u

u^{2} - 2 u = 0

Solve

u^{2} - 2 u = 0 : u = 2, u = 0

u = 2, u = 0

Substitute back

u = ln (x - 1),

solve for

x

Solve

ln (x - 1) = 2 : x = e^{2} + 1

Solve

ln (x - 1) = 0 : x = 2

x = e^{2} + 1, x = 2

Verify Solutions:

x = e^{2} + 1

True

, x = 2

True

The solutions are

x = e^{2} + 1, x = 2

lo g_{10} (a) = 11.3

x, - 1 = ln (x - y)

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

104 = 20 lo g_{10} (x)

ln (\frac{X}{0.025}) = - 1.18

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