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受欢迎的代数 >

(2^{x+1})/(4^{x-1)}=2x

解答

\frac{2 ^{x + 1}}{4 ^{x - 1}} = 2 x

解答

x = \frac{W _{0} ( 4 ln ( 2 ) )}{ln ( 2 )}

+1

十进制

x = 1.45699 \dots

求解步骤

\frac{2 ^{x + 1}}{4 ^{x - 1}} = 2 x

将

\frac{2 ^{x + 1}}{4 ^{x - 1}} = 2 x

调整为朗伯形式:

1 = e^{l n (2) (x - 2)} x

用

x ln (2) = u

和

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

改写方程式

1 = e^{l n (2) ((\frac{u}{l n ( 2 )}) - 2)} (\frac{u}{ln ( 2 )})

化简

1 = \frac{e ^{u - 2 l n (2)} u}{ln ( 2 )}

改写

1 = \frac{e ^{u - 2 l n (2)} u}{ln ( 2 )}

为朗伯形式:

e^{u} u = 4 ln (2)

解

e^{u} u = 4 ln (2) : u = W_{0} (4 ln (2))

u = W_{0} (4 ln (2))

代回

u = x ln (2)

，求解

x

解

x ln (2) = W_{0} (4 ln (2)) : x = \frac{W _{0} ( 4 ln ( 2 ) )}{ln ( 2 )}

x = \frac{W _{0} ( 4 ln ( 2 ) )}{ln ( 2 )}

验证解:

x = \frac{W _{0} ( 4 ln ( 2 ) )}{ln ( 2 )}

真

解是

x = \frac{W _{0} ( 4 ln ( 2 ) )}{ln ( 2 )}

验证解:

x = \frac{W _{0} ( 4 ln ( 2 ) )}{ln ( 2 )}

真

解是

x = \frac{W _{0} ( 4 ln ( 2 ) )}{ln ( 2 )}

作图

流行的例子

e^{2 x} - x^{3} = 0

- 4 = e^{x}

solvefor x,e^x-y^2=0

so l v e f or x, e^{x} - y^{2} = 0

\frac{18}{e ^{x} + 3} = 5

5^{x - 2} = \frac{1}{125}