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受欢迎的代数 >

g(n)=7^n,g(2)

解答

g (n) = 7^{n}, g (2)

解答

n = - \frac{W ( - \frac{l n ( 7 )}{g} )}{ln ( 7 )}

求解步骤

g (n) = 7^{n}

将

g (n) = 7^{n}

调整为朗伯形式:

g n e^{- l n (7) n} = 1

用

- n ln (7) = u

和

n = - \frac{u}{ln ( 7 )}

改写方程式

g (- \frac{u}{ln ( 7 )}) e^{u} = 1

改写

g (- \frac{u}{ln ( 7 )}) e^{u} = 1

为朗伯形式:

e^{u} u = - \frac{ln ( 7 )}{g}

解

e^{u} u = - \frac{ln ( 7 )}{g} : u = W (- \frac{ln ( 7 )}{g})

u = W (- \frac{ln ( 7 )}{g})

代回

u = - n ln (7)

，求解

n

解

- n ln (7) = W (- \frac{ln ( 7 )}{g}) : n = - \frac{W ( - \frac{l n ( 7 )}{g} )}{ln ( 7 )}

n = - \frac{W ( - \frac{l n ( 7 )}{g} )}{ln ( 7 )}

作图

流行的例子

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

256 = 4^{x}

1.2=3.3(e^{-(0.3)/x})

1.2 = 3.3 (e^{- \frac{0.3}{x}})

1.0 5^{x} = 160

x^{x} = π