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

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

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

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

x = e^{2}, x = e

Decimal Notation

x = 7.38905 \dots, x = 2.71828 \dots

Solution steps

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

Rewrite the equation with

ln (x) = u

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

Solve

u^{2} = 3 u - 2 : 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} (x) + lo g_{27} (x) = 16

b = 6 - 2.5 lo g_{4.53} (x)

lo g_{b} (2) = 1.73

ln (x + 4) = 2 ln (x) + ln (4)

x^{(l o g_{10} (x))} = 100 x

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