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受欢迎的代数 >

3^{15}k= 1/(27^k)+3

解答

3^{15} k = \frac{1}{2 7 ^{k}} + 3

解答

k = \frac{W _{0} ( \frac{l n ( 3 )}{4782969 e ^{\frac{l n ( 3 )}{1594323}}} )}{3 ln ( 3 )} + \frac{1}{4782969}

+1

十进制

k = 2.78767 E - 7

求解步骤

3^{15} k = \frac{1}{2 7 ^{k}} + 3

将

3^{15} k = \frac{1}{2 7 ^{k}} + 3

调整为朗伯形式:

1 = e^{3 l n (3) k} (14348907 k - 3)

用

3 ln (3) (k - \frac{1}{4782969}) = u

和

k = \frac{u}{3 ln ( 3 )} + \frac{1}{4782969}

改写方程式

1 = e^{3 l n (3) (\frac{u}{3 l n ( 3 )} + \frac{1}{4782969})} (14348907 (\frac{u}{3 ln ( 3 )} + \frac{1}{4782969}) - 3)

化简

1 = \frac{4782969 e ^{u + \frac{1}{1594323} l n (3)} u}{ln ( 3 )}

改写

1 = \frac{4782969 e ^{u + \frac{1}{1594323} l n (3)} u}{ln ( 3 )}

为朗伯形式:

\frac{e ^{\frac{1594323 u + l n ( 3 )}{1594323}} u}{e ^{\frac{l n ( 3 )}{1594323}}} = \frac{ln ( 3 )}{4782969 e ^{\frac{l n ( 3 )}{1594323}}}

解

\frac{e ^{\frac{1594323 u + l n ( 3 )}{1594323}} u}{e ^{\frac{l n ( 3 )}{1594323}}} = \frac{ln ( 3 )}{4782969 e ^{\frac{l n ( 3 )}{1594323}}} : u = W_{0} (\frac{ln ( 3 )}{4782969 e ^{\frac{l n ( 3 )}{1594323}}})

u = W_{0} (\frac{ln ( 3 )}{4782969 e ^{\frac{l n ( 3 )}{1594323}}})

代回

u = 3 ln (3) (k - \frac{1}{4782969})

，求解

k

解

3 ln (3) (k - \frac{1}{4782969}) = W_{0} (\frac{ln ( 3 )}{4782969 e ^{\frac{l n ( 3 )}{1594323}}}) : k = \frac{W _{0} ( \frac{l n ( 3 )}{4782969 e ^{\frac{l n ( 3 )}{1594323}}} )}{3 ln ( 3 )} + \frac{1}{4782969}

k = \frac{W _{0} ( \frac{l n ( 3 )}{4782969 e ^{\frac{l n ( 3 )}{1594323}}} )}{3 ln ( 3 )} + \frac{1}{4782969}

验证解:

k = \frac{W _{0} ( \frac{l n ( 3 )}{4782969 e ^{\frac{l n ( 3 )}{1594323}}} )}{3 ln ( 3 )} + \frac{1}{4782969}

真

解是

k = \frac{W _{0} ( \frac{l n ( 3 )}{4782969 e ^{\frac{l n ( 3 )}{1594323}}} )}{3 ln ( 3 )} + \frac{1}{4782969}

验证解:

k = \frac{W _{0} ( \frac{l n ( 3 )}{4782969 e ^{\frac{l n ( 3 )}{1594323}}} )}{3 ln ( 3 )} + \frac{1}{4782969}

真

解是

k = \frac{W _{0} ( \frac{l n ( 3 )}{4782969 e ^{\frac{l n ( 3 )}{1594323}}} )}{3 ln ( 3 )} + \frac{1}{4782969}

作图

流行的例子

(b)5^{2x+1}=125

(b) 5^{2 x + 1} = 125

7^{x} - 7^{- x} = 7

3^{x} = \frac{1}{27}

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

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

(3^{x})^{- 1} = 3