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

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

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

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

x = e^{2}, x = e

Decimal Notation

x = 7.38905 \dots, x = 2.71828 \dots

Solution steps

ln^{2} (x) - 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

1 + lo g_{6} (x) = lo g_{6} (2 x + 4)

x, lo g_{2} (x) = 4

6.01 - 9.69 = lo g_{10} (x)

lo g_{4} (2 + x) - lo g_{4} (3 - 5 x) = 3

lo g_{4} (x) + 6 lo g_{x} (4) - 5 = 0

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