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受欢迎的代数 >

2x-1sqrt(3^{x-3)}=sqrt(27)

解答

2 x - 1 3^{x - 3} = 27

解答

x = \frac{2 ln - \frac{4 W _{- 1} ( - \frac{l n ( 3 ) e ^{- \frac{6 l n ( 3 ) - 3 l n ( 3 )}{4}}}{4} )}{l n ( 3 )}}{ln ( 3 )} + 3, x = \frac{2 ln - \frac{4 W _{0} ( - \frac{l n ( 3 ) e ^{- \frac{6 l n ( 3 ) - 3 l n ( 3 )}{4}}}{4} )}{l n ( 3 )}}{ln ( 3 )} + 3

+1

十进制

x = 6.93121 \dots, x = 3.13722 \dots

求解步骤

2 x - 1 \cdot 3^{x - 3} = 27

用

3^{x - 3} = u

和

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

改写方程式

2 (\frac{2 ln ( u )}{ln ( 3 )} + 3) - 1 \cdot u = 27

解

2 (\frac{2 ln ( u )}{ln ( 3 )} + 3) - 1 \cdot u = 27 : u = - \frac{4 W _{- 1} ( - \frac{l n ( 3 )}{4 e ^{\frac{6 l n ( 3 ) - 3 3 l n ( 3 )}{4}}} )}{ln ( 3 )}, u = - \frac{4 W _{0} ( - \frac{l n ( 3 )}{4 e ^{\frac{6 l n ( 3 ) - 3 3 l n ( 3 )}{4}}} )}{ln ( 3 )}

u = - \frac{4 W _{- 1} ( - \frac{l n ( 3 )}{4 e ^{\frac{6 l n ( 3 ) - 3 3 l n ( 3 )}{4}}} )}{ln ( 3 )}, u = - \frac{4 W _{0} ( - \frac{l n ( 3 )}{4 e ^{\frac{6 l n ( 3 ) - 3 3 l n ( 3 )}{4}}} )}{ln ( 3 )}

代回

u = 3^{x - 3}

，求解

x

解

3^{x - 3} = - \frac{4 W _{- 1} ( - \frac{l n ( 3 )}{4 e ^{\frac{6 l n ( 3 ) - 3 3 l n ( 3 )}{4}}} )}{ln ( 3 )} : x = \frac{2 ln - \frac{4 W _{- 1} ( - \frac{l n ( 3 ) e ^{- \frac{6 l n ( 3 ) - 3 l n ( 3 )}{4}}}{4} )}{l n ( 3 )}}{ln ( 3 )} + 3

解

3^{x - 3} = - \frac{4 W _{0} ( - \frac{l n ( 3 )}{4 e ^{\frac{6 l n ( 3 ) - 3 3 l n ( 3 )}{4}}} )}{ln ( 3 )} : x = \frac{2 ln - \frac{4 W _{0} ( - \frac{l n ( 3 ) e ^{- \frac{6 l n ( 3 ) - 3 l n ( 3 )}{4}}}{4} )}{l n ( 3 )}}{ln ( 3 )} + 3

x = \frac{2 ln - \frac{4 W _{- 1} ( - \frac{l n ( 3 ) e ^{- \frac{6 l n ( 3 ) - 3 l n ( 3 )}{4}}}{4} )}{l n ( 3 )}}{ln ( 3 )} + 3, x = \frac{2 ln - \frac{4 W _{0} ( - \frac{l n ( 3 ) e ^{- \frac{6 l n ( 3 ) - 3 l n ( 3 )}{4}}}{4} )}{l n ( 3 )}}{ln ( 3 )} + 3

验证解:

x = \frac{2 ln - \frac{4 W _{- 1} ( - \frac{l n ( 3 ) e ^{- \frac{6 l n ( 3 ) - 3 l n ( 3 )}{4}}}{4} )}{l n ( 3 )}}{ln ( 3 )} + 3

真

, x = \frac{2 ln - \frac{4 W _{0} ( - \frac{l n ( 3 ) e ^{- \frac{6 l n ( 3 ) - 3 l n ( 3 )}{4}}}{4} )}{l n ( 3 )}}{ln ( 3 )} + 3

真

解为

x = \frac{2 ln - \frac{4 W _{- 1} ( - \frac{l n ( 3 ) e ^{- \frac{6 l n ( 3 ) - 3 l n ( 3 )}{4}}}{4} )}{l n ( 3 )}}{ln ( 3 )} + 3, x = \frac{2 ln - \frac{4 W _{0} ( - \frac{l n ( 3 ) e ^{- \frac{6 l n ( 3 ) - 3 l n ( 3 )}{4}}}{4} )}{l n ( 3 )}}{ln ( 3 )} + 3

作图

流行的例子

solvefor y,sqrt(x)+sqrt(y)=5

so l v e f or y, x + y = 5

sqrt(-2x+30)=x-3

- 2 x + 30 = x - 3

x + 3 = 2 x

3 x - 2 = 0

sqrt(7x-5)-sqrt(3x-2)=sqrt(4x-3)

7 x - 5 - 3 x - 2 = 4 x - 3