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受欢迎的代数 >

3^x=x^4

解答

3^{x} = x^{4}

解答

x = - \frac{4 W _{0} ( \frac{l n ( 3 )}{4} )}{ln ( 3 )}, x = - \frac{4 W _{0} ( - \frac{l n ( 3 )}{4} )}{ln ( 3 )}, x = - \frac{4 W _{- 1} ( - \frac{l n ( 3 )}{4} )}{ln ( 3 )}

+1

十进制

x = - 0.80224 \dots, x = 1.51677 \dots, x = 7.17475 \dots

求解步骤

3^{x} = x^{4}

对方程式两边

\frac{1}{4}

次方

(3^{x})^{\frac{1}{4}} = (x^{4})^{\frac{1}{4}}

化简

(3^{x})^{\frac{1}{4}} : 3^{\frac{x}{4}}

化简

(x^{4})^{\frac{1}{4}} : ∣ x ∣

解

3^{\frac{x}{4}} = ∣ x ∣ : x = - \frac{4 W _{0} ( \frac{l n ( 3 )}{4} )}{ln ( 3 )} or x = - \frac{4 W _{0} ( - \frac{l n ( 3 )}{4} )}{ln ( 3 )} or x = - \frac{4 W _{- 1} ( - \frac{l n ( 3 )}{4} )}{ln ( 3 )}

x = - \frac{4 W _{0} ( \frac{l n ( 3 )}{4} )}{ln ( 3 )}, x = - \frac{4 W _{0} ( - \frac{l n ( 3 )}{4} )}{ln ( 3 )}, x = - \frac{4 W _{- 1} ( - \frac{l n ( 3 )}{4} )}{ln ( 3 )}

作图

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