What is the answer to x^{12}=e^x ?

The answer to x^{12}=e^x is x=-12\W_{0}(1/12),x=-12\W_{0}(-1/12),x=-12\W_{-1}(-1/12)

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x^{12}=e^x

x^{12} = e^{x}

x = - 12 W_{0} (\frac{1}{12}), x = - 12 W_{0} (- \frac{1}{12}), x = - 12 W_{- 1} (- \frac{1}{12})

Decimal Notation

x = - 0.92575 \dots, x = 1.09559 \dots, x = 45.92380 \dots

Solution steps

x^{12} = e^{x}

Take both sides of the equation to the power of

\frac{1}{12}

(x^{12})^{\frac{1}{12}} = (e^{x})^{\frac{1}{12}}

Simplify

(x^{12})^{\frac{1}{12}} : ∣ x ∣

Simplify

(e^{x})^{\frac{1}{12}} : e^{\frac{x}{12}}

Solve

∣ x ∣ = e^{\frac{x}{12}} : x = - 12 W_{0} (\frac{1}{12}) or x = - 12 W_{0} (- \frac{1}{12}) or x = - 12 W_{- 1} (- \frac{1}{12})

x = - 12 W_{0} (\frac{1}{12}), x = - 12 W_{0} (- \frac{1}{12}), x = - 12 W_{- 1} (- \frac{1}{12})

9^{x - 1} = 3^{1 + x}

2^{x} = \frac{8 ^{x}}{e}

y, e^{x + y} = y

8 \cdot 3^{x} = 1

What is the answer to x^{12}=e^x ?
The answer to x^{12}=e^x is x=-12\W_{0}(1/12),x=-12\W_{0}(-1/12),x=-12\W_{-1}(-1/12)