What is the answer to x^{10}=e^x ?

The answer to x^{10}=e^x is x=-10\W_{0}(1/10),x=-10\W_{0}(-1/10),x=-10\W_{-1}(-1/10)

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x^{10}=e^x

x^{10} = e^{x}

x = - 10 W_{0} (\frac{1}{10}), x = - 10 W_{0} (- \frac{1}{10}), x = - 10 W_{- 1} (- \frac{1}{10})

Decimal Notation

x = - 0.91276 \dots, x = 1.11832 \dots, x = 35.77152 \dots

Solution steps

x^{10} = e^{x}

Take both sides of the equation to the power of

\frac{1}{10}

(x^{10})^{\frac{1}{10}} = (e^{x})^{\frac{1}{10}}

Simplify

(x^{10})^{\frac{1}{10}} : ∣ x ∣

Simplify

(e^{x})^{\frac{1}{10}} : e^{\frac{x}{10}}

Solve

∣ x ∣ = e^{\frac{x}{10}} : x = - 10 W_{0} (\frac{1}{10}) or x = - 10 W_{0} (- \frac{1}{10}) or x = - 10 W_{- 1} (- \frac{1}{10})

x = - 10 W_{0} (\frac{1}{10}), x = - 10 W_{0} (- \frac{1}{10}), x = - 10 W_{- 1} (- \frac{1}{10})

4^{x} = \frac{8}{1 6 ^{x}}

x, e^{x} = 4

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

e^{x - 1} = 3^{\frac{2 x}{3}}

2^{(1 - x)} + 2^{(1 + x)} = 4

What is the answer to x^{10}=e^x ?
The answer to x^{10}=e^x is x=-10\W_{0}(1/10),x=-10\W_{0}(-1/10),x=-10\W_{-1}(-1/10)