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

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

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

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

x = e^{2}, x = e

Decimal Notation

x = 7.38905 \dots, x = 2.71828 \dots

Solution steps

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

Rewrite the equation with

ln (x) = u

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

Solve

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

u = 2, u = 1

Substitute back

u = ln (x),

solve for

x

Solve

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

Solve

ln (x) = 1 : x = e

x = e^{2}, x = e

Verify Solutions:

x = e^{2}

True

, x = e

True

The solutions are

x = e^{2}, x = e

lo g_{3} (8 x + 1) - lo g_{3} (x) = 1

0.3 = ln (x)

ln (x) - 3 = ln (\frac{1}{x})

x, lo g_{4} (8 x + 3) = 1

2 ln (x) - ln (x^{2} + x - 3) = ln (1)

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