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受欢迎的代数 >

1.02^n+50*n=-200

解答

1.0 2^{n} + 50 \cdot n = - 200

解答

n = - \frac{W _{0} ( \frac{l n ( 1.02 )}{54.121608} ) + 4 ln ( 1.02 )}{ln ( 1.02 )}

+1

十进制

n = - 4.01847 \dots

求解步骤

1.0 2^{n} + 50 n = - 200

将

1.0 2^{n} + 50 \cdot n = - 200

调整为朗伯形式:

1 = (- 200 - 50 n) e^{- l n (1.02) n}

用

(- n - 4) ln (1.02) = u

和

n = - \frac{u + 4 ln ( 1.02 )}{ln ( 1.02 )}

改写方程式

1 = (- 200 - 50 (- \frac{u + 4 ln ( 1.02 )}{ln ( 1.02 )})) e^{- l n (1.02) (- \frac{u + 4 l n ( 1.02 )}{l n ( 1.02 )})}

化简

1 = e^{u + 4 l n (1.02)} (- 200 + \frac{50 ( u + 4 ln ( 1.02 ) )}{ln ( 1.02 )})

改写

1 = e^{u + 4 l n (1.02)} (- 200 + \frac{50 ( u + 4 ln ( 1.02 ) )}{ln ( 1.02 )})

为朗伯形式:

e^{u} u = \frac{ln ( 1.02 )}{54.121608}

解

e^{u} u = \frac{ln ( 1.02 )}{54.121608} : u = W_{0} (\frac{ln ( 1.02 )}{54.121608})

u = W_{0} (\frac{ln ( 1.02 )}{54.121608})

代回

u = (- n - 4) ln (1.02)

，求解

n

解

(- n - 4) ln (1.02) = W_{0} (\frac{ln ( 1.02 )}{54.121608}) : n = - \frac{W _{0} ( \frac{l n ( 1.02 )}{54.121608} ) + 4 ln ( 1.02 )}{ln ( 1.02 )}

n = - \frac{W _{0} ( \frac{l n ( 1.02 )}{54.121608} ) + 4 ln ( 1.02 )}{ln ( 1.02 )}

作图

流行的例子

2^{3x-13}= 1/16

2^{3 x - 13} = \frac{1}{16}

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

4^{c} = 64

3^{x - 2} = \frac{1}{81}

solvefor x,2^{x-5}=5

so l v e f or x, 2^{x - 5} = 5