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

(ln (x))^{2} = 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

lo g_{x} (\frac{1}{9}) = 2

\frac{ln ( 3 x - 1 )}{ln ( x - 1 )} = 3

lo g_{10} (x) + lo g_{10} (x + 48) = 2

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

3 lo g_{2} (x) - 2 lo g_{2} (5 x) = 2

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