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

The answer to 2ln(x)-(ln(x))^2=0 is x=1,x=e^2

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2ln(x)-(ln(x))^2=0

2 ln (x) - (ln (x))^{2} = 0

x = 1, x = e^{2}

Decimal Notation

x = 1, x = 7.38905 \dots

Solution steps

2 ln (x) - (ln (x))^{2} = 0

Rewrite the equation with

ln (x) = u

2 u - (u)^{2} = 0

Solve

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

u = 0, u = 2

Substitute back

u = ln (x),

solve for

x

Solve

ln (x) = 0 : x = 1

Solve

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

x = 1, x = e^{2}

Verify Solutions:

x = 1

True

, x = e^{2}

True

The solutions are

x = 1, x = e^{2}

lo g_{4} (x + 2) + lo g_{2} (4) = 0

lo g_{3} (x - 4) + lo g_{3} (x + 6) = 1

lo g_{x} (1.41) = 0.5

- 3 = 20 lo g_{10} (x)

lo g_{5} (x + 1) = 2 + lo g_{5} (x - 1)

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