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

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

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

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

x = 1, x = e

Decimal Notation

x = 1, x = 2.71828 \dots

Solution steps

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

Rewrite the equation with

ln (x) = u

u^{2} = u^{3}

Solve

u^{2} = u^{3} : u = 0, u = 1

u = 0, u = 1

Substitute back

u = ln (x),

solve for

x

Solve

ln (x) = 0 : x = 1

Solve

ln (x) = 1 : x = e

x = 1, x = e

Verify Solutions:

x = 1

True

, x = e

True

The solutions are

x = 1, x = e

y, 3 ln (x + 4) = ln (y)

lo g_{y} (81) = - 4

10 = lo g_{2} (64 x)

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

lo g_{2} (x) = 939143.50112

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