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

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

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(ln(x))^2=2ln(x)

(ln (x))^{2} = 2 ln (x)

x = e^{2}, x = 1

Decimal Notation

x = 7.38905 \dots, x = 1

Solution steps

(ln (x))^{2} = 2 ln (x)

Rewrite the equation with

ln (x) = u

(u)^{2} = 2 u

Solve

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

u = 2, u = 0

Substitute back

u = ln (x),

solve for

x

Solve

ln (x) = 2 : x = e^{2}

Solve

ln (x) = 0 : x = 1

x = e^{2}, x = 1

Verify Solutions:

x = e^{2}

True

, x = 1

True

The solutions are

x = e^{2}, x = 1

y, lo g_{3} (y) = x

lo g_{10} (x + 3) = 2

ln (x + 3) - ln (x - 2) = ln (x)

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

x, 2 = - lo g_{10} (x)

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