What is the answer to ln^2(x)-ln(x)=6 ?

The answer to ln^2(x)-ln(x)=6 is x=e^3,x= 1/(e^2)

Solve for x: ln^2(x)-ln(x)=6

The solution is x=e^3,x= 1/(e^2)

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ln^{2} (x) - ln (x) = 6

x = e^{3}, x = \frac{1}{e ^{2}}

Decimal Notation

x = 20.08553 \dots, x = 0.13533 \dots

Solution steps

ln^{2} (x) - ln (x) = 6

Rewrite the equation with

ln (x) = u

u^{2} - u = 6

Solve

u^{2} - u = 6 : u = 3, u = - 2

u = 3, u = - 2

Substitute back

u = ln (x),

solve for

x

Solve

ln (x) = 3 : x = e^{3}

Solve

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

x = e^{3}, x = \frac{1}{e ^{2}}

Verify Solutions:

x = e^{3}

True

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

True

The solutions are

x = e^{3}, x = \frac{1}{e ^{2}}

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

lo g_{x} (128) = \frac{1}{2}

x^{3} ln (x) = 0

lo g_{3} (a) = 4 lo g_{3} (x)

lo g_{4} (x - 7) = 3

What is the answer to ln^2(x)-ln(x)=6 ?
The answer to ln^2(x)-ln(x)=6 is x=e^3,x= 1/(e^2)
Solve for x: ln^2(x)-ln(x)=6
The solution is x=e^3,x= 1/(e^2)