zs

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

受欢迎的代数 >

4^2x+8=3(8^x)

解答

4^{2} x + 8 = 3 (8^{x})

解答

x = - \frac{2 W _{- 1} ( - \frac{9 l n ( 2 )}{16 e ^{\frac{3 l n ( 2 )}{2}}} ) + 3 ln ( 2 )}{6 ln ( 2 )}, x = - \frac{2 W _{0} ( - \frac{9 l n ( 2 )}{16 e ^{\frac{3 l n ( 2 )}{2}}} ) + 3 ln ( 2 )}{6 ln ( 2 )}

+1

十进制

x = 1, x = - 0.42204 \dots

求解步骤

4^{2} x + 8 = 3 (8^{x})

将

4^{2} x + 8 = 3 (8^{x})

调整为朗伯形式:

e^{- 3 l n (2) x} (16 x + 8) = 3

用

3 ln (2) (- x - \frac{1}{2}) = u

和

x = - \frac{2 u + 3 ln ( 2 )}{6 ln ( 2 )}

改写方程式

e^{- 3 l n (2) (- \frac{2 u + 3 l n ( 2 )}{6 l n ( 2 )})} (16 (- \frac{2 u + 3 ln ( 2 )}{6 ln ( 2 )}) + 8) = 3

化简

e^{\frac{2 u + 3 l n ( 2 )}{2}} (- \frac{8 ( 2 u + 3 ln ( 2 ) )}{3 ln ( 2 )} + 8) = 3

改写

e^{\frac{2 u + 3 l n ( 2 )}{2}} (- \frac{8 ( 2 u + 3 ln ( 2 ) )}{3 ln ( 2 )} + 8) = 3

为朗伯形式:

\frac{e ^{\frac{2 u + 3 l n ( 2 )}{2}} u}{e ^{\frac{3 l n ( 2 )}{2}}} = - \frac{9 ln ( 2 )}{16 e ^{\frac{3 l n ( 2 )}{2}}}

解

\frac{e ^{\frac{2 u + 3 l n ( 2 )}{2}} u}{e ^{\frac{3 l n ( 2 )}{2}}} = - \frac{9 ln ( 2 )}{16 e ^{\frac{3 l n ( 2 )}{2}}} : u = W_{- 1} (- \frac{9 ln ( 2 )}{16 e ^{\frac{3 l n ( 2 )}{2}}}), u = W_{0} (- \frac{9 ln ( 2 )}{16 e ^{\frac{3 l n ( 2 )}{2}}})

u = W_{- 1} (- \frac{9 ln ( 2 )}{16 e ^{\frac{3 l n ( 2 )}{2}}}), u = W_{0} (- \frac{9 ln ( 2 )}{16 e ^{\frac{3 l n ( 2 )}{2}}})

代回

u = 3 ln (2) (- x - \frac{1}{2})

，求解

x

解

3 ln (2) (- x - \frac{1}{2}) = W_{- 1} (- \frac{9 ln ( 2 )}{16 e ^{\frac{3 l n ( 2 )}{2}}}) : x = - \frac{2 W _{- 1} ( - \frac{9 l n ( 2 )}{16 e ^{\frac{3 l n ( 2 )}{2}}} ) + 3 ln ( 2 )}{6 ln ( 2 )}

解

3 ln (2) (- x - \frac{1}{2}) = W_{0} (- \frac{9 ln ( 2 )}{16 e ^{\frac{3 l n ( 2 )}{2}}}) : x = - \frac{2 W _{0} ( - \frac{9 l n ( 2 )}{16 e ^{\frac{3 l n ( 2 )}{2}}} ) + 3 ln ( 2 )}{6 ln ( 2 )}

x = - \frac{2 W _{- 1} ( - \frac{9 l n ( 2 )}{16 e ^{\frac{3 l n ( 2 )}{2}}} ) + 3 ln ( 2 )}{6 ln ( 2 )}, x = - \frac{2 W _{0} ( - \frac{9 l n ( 2 )}{16 e ^{\frac{3 l n ( 2 )}{2}}} ) + 3 ln ( 2 )}{6 ln ( 2 )}

作图

流行的例子

4^{x} = 64

4^{2x+1}+7(4^x)-15=0

4^{2 x + 1} + 7 (4^{x}) - 15 = 0

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

log_{4}(2^{4x})=2^{log_{2}(4)}

lo g_{4} (2^{4 x}) = 2^{l o g_{2} (4)}

5^{2x-1}=2^{x+1}

5^{2 x - 1} = 2^{x + 1}