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

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

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

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

x = e^{2}, x = 1

Solution steps

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

Apply log rules

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

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_{x} (3^{x}) = \frac{x}{2}

lo g_{x + 1} (4) = 2

0.23 = ln (y)

lo g_{10} (- x - 4) = 2

50 = - 23.98 ln (x) + 33.243

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