What is the answer to (ln(x))^2-2ln(x)-3=0 ?

The answer to (ln(x))^2-2ln(x)-3=0 is x=e^3,x= 1/e

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(ln(x))^2-2ln(x)-3=0

(ln (x))^{2} - 2 ln (x) - 3 = 0

x = e^{3}, x = \frac{1}{e}

Decimal Notation

x = 20.08553 \dots, x = 0.36787 \dots

Solution steps

(ln (x))^{2} - 2 ln (x) - 3 = 0

Rewrite the equation with

ln (x) = u

(u)^{2} - 2 u - 3 = 0

Solve

u^{2} - 2 u - 3 = 0 : u = 3, u = - 1

u = 3, u = - 1

Substitute back

u = ln (x),

solve for

x

Solve

ln (x) = 3 : x = e^{3}

Solve

ln (x) = - 1 : x = \frac{1}{e}

x = e^{3}, x = \frac{1}{e}

Verify Solutions:

x = e^{3}

True

, x = \frac{1}{e}

True

The solutions are

x = e^{3}, x = \frac{1}{e}

x, ln (x) = ln (y) + c

lo g_{10} (x + 9) - lo g_{10} (x) = 3

lo g_{x^{3}} (64) = \frac{2}{3}

ln (x) = \infty

8 = lo g_{10} (x)

What is the answer to (ln(x))^2-2ln(x)-3=0 ?
The answer to (ln(x))^2-2ln(x)-3=0 is x=e^3,x= 1/e
Solve for x: (ln(x))^2-2ln(x)-3=0
The solution is x=e^3,x= 1/e