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

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

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

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

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

Decimal Notation

x = 1, x = 0.04978 \dots

Solution steps

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

Rewrite the equation with

ln (x) = u

u^{3} + 3 u^{2} = 0

Solve

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

u = 0, u = - 3

Substitute back

u = ln (x),

solve for

x

Solve

ln (x) = 0 : x = 1

Solve

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

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

Verify Solutions:

x = 1

True

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

True

The solutions are

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

ln (3 x - 16) = 9

x, ln (e^{x y}) = ln (1)

ln (3 x - 16) = 6

20 lo g_{10} (\frac{x}{1}) = 30

0 = 2 x + ln (x)

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