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 >

23^x-32^y=42,3^{x+1}-2^{y+1}=73

解答

2 \cdot 3^{x} - 3 \cdot 2^{y} = 42, 3^{x + 1} - 2^{y + 1} = 73

解答

(x = 3, y = 2)

求解步骤

[2 \cdot 3^{x} - 3 \cdot 2^{y} = 42 3^{x + 1} - 2^{y + 1} = 73]

对于

2 \cdot 3^{x} - 3 \cdot 2^{y} = 42

将

x

移到一边:

x = \frac{ln ( \frac{42 + 3 \cdot 2 ^{y}}{2} )}{ln ( 3 )}

将解

x = \frac{ln ( \frac{42 + 3 \cdot 2 ^{y}}{2} )}{ln ( 3 )}

代入

3^{x + 1} - 2^{y + 1} = 73

对于

3^{x + 1} - 2^{y + 1} = 73

，用

\frac{ln ( \frac{42 + 3 \cdot 2 ^{y}}{2} )}{ln ( 3 )}

替代

x : y = 2

将解

y = 2

代入

2 \cdot 3^{x} - 3 \cdot 2^{y} = 42

对于

2 \cdot 3^{x} - 3 \cdot 2^{y} = 42

，用

2

替代

y : x = 3

将解代入原方程进行验证

因而，

2 \cdot 3^{x} - 3 \cdot 2^{y} = 42, 3^{x + 1} - 2^{y + 1} = 73

最后的解是

(x = 3, y = 2)

作图

流行的例子

5/((x-1))+1/((y-2))=2, 6/((x-1))-3/((y-2))=1

\frac{5}{( x - 1 )} + \frac{1}{( y - 2 )} = 2, \frac{6}{( x - 1 )} - \frac{3}{( y - 2 )} = 1

x - y = 6, x + y = 12

5x+y=22,3x+y=14

5 x + y = 22, 3 x + y = 14

-8y+9x=5,8y+7x=-75

- 8 y + 9 x = 5, 8 y + 7 x = - 75

2x-3y=4,x+5y=15

2 x - 3 y = 4, x + 5 y = 15