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

The answer to ln(x^2)=x is x=-2\W_{0}(1/2)

Solve for x: ln(x^2)=x

The solution is x=-2\W_{0}(1/2)

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ln (x^{2}) = x

x = - 2 W_{0} (\frac{1}{2})

Decimal

x = - 0.70346 \dots

Solution steps

ln (x^{2}) = x

f (x) = g (x),

then

a^{f (x)} = a^{g (x)}

e^{l n (x^{2})} = e^{x}

Simplify

e^{l n (x^{2})} : x^{2}

x^{2} = e^{x}

Solve

x^{2} = e^{x} : x = - 2 W_{0} (\frac{1}{2})

x = - 2 W_{0} (\frac{1}{2})

Verify Solutions:

x = - 2 W_{0} (\frac{1}{2})

True

The solution is

x = - 2 W_{0} (\frac{1}{2})

lo g_{3} (x) = lo g_{4} (x)

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

ln (2 x - 3) = 5

ln (3 x - 7) = 4

ln (x^{2}) = 3