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

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

Solve for x: ln^2(x)+ln(x^3)+2=0

The solution is x= 1/e ,x= 1/(e^2)

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

x = \frac{1}{e}, x = \frac{1}{e ^{2}}

Decimal

x = 0.36787 \dots, x = 0.13533 \dots

Solution steps

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

Apply log rules

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 = - 1, u = - 2

u = - 1, u = - 2

Substitute back

u = ln (x),

solve for

x

Solve

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

Solve

ln (x) = - 2 : x = \frac{1}{e ^{2}}

x = \frac{1}{e}, x = \frac{1}{e ^{2}}

Verify Solutions:

x = \frac{1}{e}

True

, x = \frac{1}{e ^{2}}

True

The solutions are

x = \frac{1}{e}, x = \frac{1}{e ^{2}}

lo g_{3} (x) = - \frac{1}{4}

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

lo g_{9} (a) = 2

2 = lo g_{3} (t)

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

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