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

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

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

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

x = e^{2}, x = 1

Decimal Notation

x = 7.38905 \dots, x = 1

Solution steps

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

Apply log rules

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

Rewrite the equation with

ln (x) = u

2 u = (u)^{2}

Solve

2 u = u^{2} : 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

lo g_{10} (c) = 10

lo g_{10} (2 x) = 4

lo g_{4} (x) = 1

lo g_{9} (x^{2} - 10) = 1

ln^{2} (x) = 0

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