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人気のある代数 >

x^{10}=2^x

解

x^{10} = 2^{x}

解

x = - \frac{10 W _{0} ( \frac{l n ( 2 )}{10} )}{ln ( 2 )}, x = - \frac{10 W _{0} ( - \frac{l n ( 2 )}{10} )}{ln ( 2 )}, x = - \frac{10 W _{- 1} ( - \frac{l n ( 2 )}{10} )}{ln ( 2 )}

+1

十進法表記

x = - 0.93710 \dots, x = 1.07755 \dots, x = 58.77010 \dots

解答ステップ

x^{10} = 2^{x}

equationの両辺を以下の累乗にする:

\frac{1}{10}

(x^{10})^{\frac{1}{10}} = (2^{x})^{\frac{1}{10}}

簡素化

(x^{10})^{\frac{1}{10}} : ∣ x ∣

簡素化

(2^{x})^{\frac{1}{10}} : 2^{\frac{x}{10}}

解く

∣ x ∣ = 2^{\frac{x}{10}} : x = - \frac{10 W _{0} ( \frac{l n ( 2 )}{10} )}{ln ( 2 )} or x = - \frac{10 W _{0} ( - \frac{l n ( 2 )}{10} )}{ln ( 2 )} or x = - \frac{10 W _{- 1} ( - \frac{l n ( 2 )}{10} )}{ln ( 2 )}

x = - \frac{10 W _{0} ( \frac{l n ( 2 )}{10} )}{ln ( 2 )}, x = - \frac{10 W _{0} ( - \frac{l n ( 2 )}{10} )}{ln ( 2 )}, x = - \frac{10 W _{- 1} ( - \frac{l n ( 2 )}{10} )}{ln ( 2 )}

グラフ

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