What is the answer to x^8=e^x ?

The answer to x^8=e^x is x=-8\W_{0}(1/8),x=-8\W_{0}(-1/8),x=-8\W_{-1}(-1/8)

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x^8=e^x

x^{8} = e^{x}

x = - 8 W_{0} (\frac{1}{8}), x = - 8 W_{0} (- \frac{1}{8}), x = - 8 W_{- 1} (- \frac{1}{8})

Decimal Notation

x = - 0.89424 \dots, x = 1.15537 \dots, x = 26.09348 \dots

Solution steps

x^{8} = e^{x}

Take both sides of the equation to the power of

\frac{1}{8}

(x^{8})^{\frac{1}{8}} = (e^{x})^{\frac{1}{8}}

Simplify

(x^{8})^{\frac{1}{8}} : ∣ x ∣

Simplify

(e^{x})^{\frac{1}{8}} : e^{\frac{x}{8}}

Solve

∣ x ∣ = e^{\frac{x}{8}} : x = - 8 W_{0} (\frac{1}{8}) or x = - 8 W_{0} (- \frac{1}{8}) or x = - 8 W_{- 1} (- \frac{1}{8})

x = - 8 W_{0} (\frac{1}{8}), x = - 8 W_{0} (- \frac{1}{8}), x = - 8 W_{- 1} (- \frac{1}{8})

x, e^{x} = 5

\frac{1}{8} = 2^{n}

9^{x} = 3^{1 - 2 x}

8 e^{2 x} = 20

6^{12 x} = 6^{13 x} + 4

What is the answer to x^8=e^x ?
The answer to x^8=e^x is x=-8\W_{0}(1/8),x=-8\W_{0}(-1/8),x=-8\W_{-1}(-1/8)