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

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

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

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

x = 1, x = e^{2}

Decimal Notation

x = 1, x = 7.38905 \dots

Solution steps

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

Rewrite the equation with

ln (x) = u

uu = 2 u

Solve

uu = 2 u : u = 0, u = 2

u = 0, u = 2

Substitute back

u = ln (x),

solve for

x

Solve

ln (x) = 0 : x = 1

Solve

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

x = 1, x = e^{2}

Verify Solutions:

x = 1

True

, x = e^{2}

True

The solutions are

x = 1, x = e^{2}

lo g_{10} (3 x) = 0.85

lo g_{3} (3^{x^{2} - 2 x}) = 0

lo g_{10} (0.01 x) = - 3

lo g_{10} (b) 3125 = - 5

x, 10 = ln (x \cdot y)

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