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受欢迎的代数 >

x^{10}=2^x

解答

x^{10} = 2^{x}

解答

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

十进制

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

求解步骤

x^{10} = 2^{x}

对方程式两边

\frac{1}{10}

次方

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

化简

(x^{10})^{\frac{1}{10}} : ∣ x ∣

化简

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

解

∣ 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 )}

作图

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