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

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

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

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

x = e^{2}, x = 1

Solution steps

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

Rewrite the equation with

ln (x) = u

u^{2} = 2 u

Solve

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

u = 2, u = 0

Substitute back

u = ln (x),

solve for

x

Solve

ln (x) = 2 : x = e^{2}

Solve

ln (x) = 0 : x = 1

x = e^{2}, x = 1

Verify Solutions:

x = e^{2}

True

, x = 1

True

The solutions are

x = e^{2}, x = 1

x, 2 lo g_{3} (x + 28) = 6

ln (x) = 5.912558418

lo g_{2} (x + 5) = 2

2 ln (6 - x) = ln (x - 4)

lo g_{2 x - 6} (3 x^{2} - 10 x - 12) = 2

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