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

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

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

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

x = e + 1

Decimal Notation

x = 3.71828 \dots

Solution steps

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

Rewrite the equation with

ln (x - 1) = u

u (u - 2) = - 1

Solve

u (u - 2) = - 1 : u = 1

u = 1

Substitute back

u = ln (x - 1),

solve for

x

Solve

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

x = e + 1

Verify Solutions:

x = e + 1

True

The solution is

x = e + 1

lo g_{10} (3 x) + lo g_{10} (5) = 1

11 = - lo g_{10} (x)

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

lo g_{2} (y) = 2

lo g_{2} (x) = 2 + lo g_{8} (x)

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