zs

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

受欢迎的代数 >

0.9711n-0.9711=(0.9614)^n

解答

0.9711 n - 0.9711 = (0.9614)^{n}

解答

n = - \frac{W _{0} ( - \frac{0.92428996 l n ( 0.9614 )}{0.93361554} ) - ln ( 0.9614 )}{ln ( 0.9614 )}

+1

十进制

n = 1.95353 \dots

求解步骤

0.9711 n - 0.9711 = (0.9614)^{n}

将

0.9711 n - 0.9711 = (0.9614)^{n}

调整为朗伯形式:

1 = 0.9711 (n - 1) e^{- l n (0.9614) n}

用

(- n + 1) ln (0.9614) = u

和

n = - \frac{u - ln ( 0.9614 )}{ln ( 0.9614 )}

改写方程式

1 = 0.9711 ((- \frac{u - ln ( 0.9614 )}{ln ( 0.9614 )}) - 1) e^{- l n (0.9614) (- \frac{u - l n ( 0.9614 )}{l n ( 0.9614 )})}

化简

1 = 0.9711 e^{u - l n (0.9614)} (- \frac{u - ln ( 0.9614 )}{ln ( 0.9614 )} - 1)

改写

1 = 0.9711 e^{u - l n (0.9614)} (- \frac{u - ln ( 0.9614 )}{ln ( 0.9614 )} - 1)

为朗伯形式:

e^{u} u = - \frac{0.92428996 ln ( 0.9614 )}{0.93361554}

解

e^{u} u = - \frac{0.92428996 ln ( 0.9614 )}{0.93361554} : u = W_{0} (- \frac{0.92428996 ln ( 0.9614 )}{0.93361554})

u = W_{0} (- \frac{0.92428996 ln ( 0.9614 )}{0.93361554})

代回

u = (- n + 1) ln (0.9614)

，求解

n

解

(- n + 1) ln (0.9614) = W_{0} (- \frac{0.92428996 ln ( 0.9614 )}{0.93361554}) : n = - \frac{W _{0} ( - \frac{0.92428996 l n ( 0.9614 )}{0.93361554} ) - ln ( 0.9614 )}{ln ( 0.9614 )}

n = - \frac{W _{0} ( - \frac{0.92428996 l n ( 0.9614 )}{0.93361554} ) - ln ( 0.9614 )}{ln ( 0.9614 )}

作图

流行的例子

256^{2x-16}=(1/128)^{20-2x}

25 6^{2 x - 16} = (\frac{1}{128})^{20 - 2 x}

(2^8}{3^8}=(\frac{-2)/3)^{n-1}

\frac{2 ^{8}}{3 ^{8}} = (\frac{- 2}{3})^{n - 1}

3^{x} - 1 = 0

((64*4^{3n}+4*4^{3n+3}))/((16*4^{2n)-16^n)}= 256/3

\frac{( 64 \cdot 4 ^{3 n} + 4 \cdot 4 ^{3 n + 3} )}{( 16 \cdot 4 ^{2 n} - 1 6 ^{n} )} = \frac{256}{3}

4^{x+2}+4^x=1088

4^{x + 2} + 4^{x} = 1088