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受欢迎的三角函数 >

75=50cosh(x/(50))

解答

75 = 50 cosh (\frac{x}{50})

解答

x = 50 ln (\frac{3 + 5}{2})

+1

度数

x = 2757.14066 \dots^{\circ}

求解步骤

75 = 50 cosh (\frac{x}{50})

交换两边

50 cosh (\frac{x}{50}) = 75

使用三角恒等式改写

50 cosh (\frac{x}{50}) = 75

使用双曲函数恒等式:

cosh (x) = \frac{e ^{x} + e ^{- x}}{2}

50 \cdot \frac{e ^{\frac{x}{50}} + e ^{- \frac{x}{50}}}{2} = 75

50 \cdot \frac{e ^{\frac{x}{50}} + e ^{- \frac{x}{50}}}{2} = 75

50 \cdot \frac{e ^{\frac{x}{50}} + e ^{- \frac{x}{50}}}{2} = 75 : x = 50 ln (\frac{3 + 5}{2})

50 \cdot \frac{e ^{\frac{x}{50}} + e ^{- \frac{x}{50}}}{2} = 75

使用指数运算法则

50 \cdot \frac{e ^{\frac{x}{50}} + e ^{- \frac{x}{50}}}{2} = 75

使用指数法则:

a^{b c} = (a^{b})^{c}

e^{\frac{x}{50}} = (e^{x})^{0.02}, e^{- \frac{x}{50}} = (e^{x})^{- 0.02}

50 \cdot \frac{( e ^{x} ) ^{0.02} + ( e ^{x} ) ^{- 0.02}}{2} = 75

50 \cdot \frac{( e ^{x} ) ^{0.02} + ( e ^{x} ) ^{- 0.02}}{2} = 75

用

e^{x} = u

改写方程式

50 \cdot \frac{( u ) ^{0.02} + ( u ) ^{- 0.02}}{2} = 75

解

50 \cdot \frac{u ^{0.02} + u ^{- 0.02}}{2} = 75 : u = \frac{( 3 + 5 ) ^{50}}{2 ^{50}}, u = \frac{( 3 - 5 ) ^{50}}{2 ^{50}}

50 \cdot \frac{u ^{0.02} + u ^{- 0.02}}{2} = 75

展开

50 \cdot \frac{u ^{0.02} + u ^{- 0.02}}{2} : 25 u^{0.02} + \frac{25}{u ^{0.02}}

50 \cdot \frac{u ^{0.02} + u ^{- 0.02}}{2}

\frac{u ^{0.02} + u ^{- 0.02}}{2} = \frac{u ^{0.04} + 1}{2 u ^{0.02}}

\frac{u ^{0.02} + u ^{- 0.02}}{2}

使用指数法则:

a^{- b} = \frac{1}{a ^{b}}

= \frac{u ^{0.02} + \frac{1}{u ^{0.02}}}{2}

化简

u^{0.02} + \frac{1}{u ^{0.02}} : \frac{u ^{0.04} + 1}{u ^{0.02}}

u^{0.02} + \frac{1}{u ^{0.02}}

将项转换为分式:

u^{0.02} = \frac{u ^{0.02} u ^{0.02}}{u ^{0.02}}

= \frac{u ^{0.02} u ^{0.02}}{u ^{0.02}} + \frac{1}{u ^{0.02}}

因为分母相等，所以合并分式:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{u ^{0.02} u ^{0.02} + 1}{u ^{0.02}}

u^{0.02} u^{0.02} + 1 = u^{0.04} + 1

u^{0.02} u^{0.02} + 1

u^{0.02} u^{0.02} = u^{0.04}

u^{0.02} u^{0.02}

使用指数法则:

a^{b} \cdot a^{c} = a^{b + c}

u^{0.02} u^{0.02} = u^{0.02 + 0.02}

= u^{0.02 + 0.02}

数字相加:

0.02 + 0.02 = 0.04

= u^{0.04}

= u^{0.04} + 1

= \frac{u ^{0.04} + 1}{u ^{0.02}}

= \frac{\frac{u ^{0.04} + 1}{u ^{0.02}}}{2}

使用分式法则:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= \frac{u ^{0.04} + 1}{u ^{0.02} \cdot 2}

= 50 \cdot \frac{u ^{0.04} + 1}{2 u ^{0.02}}

分式相乘:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{( u ^{0.04} + 1 ) \cdot 50}{u ^{0.02} \cdot 2}

数字相除:

\frac{50}{2} = 25

= \frac{25 ( u ^{0.04} + 1 )}{u ^{0.02}}

乘开

25 (u^{0.04} + 1) : 25 u^{0.04} + 25

25 (u^{0.04} + 1)

使用分配律:

a (b + c) = ab + a c

a = 25, b = u^{0.04}, c = 1

= 25 u^{0.04} + 25 \cdot 1

数字相乘:

25 \cdot 1 = 25

= 25 u^{0.04} + 25

= \frac{25 u ^{0.04} + 25}{u ^{0.02}}

使用分式法则:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{25 u ^{0.04} + 25}{u ^{0.02}} = \frac{25 u ^{0.04}}{u ^{0.02}} + \frac{25}{u ^{0.02}}

= \frac{25 u ^{0.04}}{u ^{0.02}} + \frac{25}{u ^{0.02}}

消掉

\frac{25 u ^{0.04}}{u ^{0.02}} : 25 u^{0.02}

\frac{25 u ^{0.04}}{u ^{0.02}}

消掉

\frac{25 u ^{0.04}}{u ^{0.02}} : 25 u^{0.02}

\frac{25 u ^{0.04}}{u ^{0.02}}

使用指数法则:

\frac{x ^{a}}{x ^{b}} = x^{a - b}

\frac{u ^{0.04}}{u ^{0.02}} = u^{0.04 - 0.02}

= 25 u^{0.04 - 0.02}

数字相减:

0.04 - 0.02 = 0.02

= 25 u^{0.02}

= 25 u^{0.02}

= 25 u^{0.02} + \frac{25}{u ^{0.02}}

25 u^{0.02} + \frac{25}{u ^{0.02}} = 75

用

u^{\frac{1}{50}} = v

改写方程式

25 v + \frac{25}{v} = 75

解

25 v + \frac{25}{v} = 75 : v = \frac{3 + 5}{2}, v = \frac{3 - 5}{2}

25 v + \frac{25}{v} = 75

在两边乘以

v

25 v + \frac{25}{v} = 75

在两边乘以

v

25 vv + \frac{25}{v} v = 75 v

化简

25 vv + \frac{25}{v} v = 75 v

化简

25 vv : 25 v^{2}

25 vv

使用指数法则:

a^{b} \cdot a^{c} = a^{b + c}

vv = v^{1 + 1}

= 25 v^{1 + 1}

数字相加:

1 + 1 = 2

= 25 v^{2}

化简

\frac{25}{v} v : 25

\frac{25}{v} v

分式相乘:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{25 v}{v}

约分:

v

= 25

25 v^{2} + 25 = 75 v

25 v^{2} + 25 = 75 v

25 v^{2} + 25 = 75 v

解

25 v^{2} + 25 = 75 v : v = \frac{3 + 5}{2}, v = \frac{3 - 5}{2}

25 v^{2} + 25 = 75 v

将

75 v

para o lado esquerdo

25 v^{2} + 25 = 75 v

两边减去

75 v

25 v^{2} + 25 - 75 v = 75 v - 75 v

化简

25 v^{2} + 25 - 75 v = 0

25 v^{2} + 25 - 75 v = 0

改写成标准形式

a x^{2} + b x + c = 0

25 v^{2} - 75 v + 25 = 0

使用求根公式求解

25 v^{2} - 75 v + 25 = 0

二次方程求根公式:

若

a = 25, b = - 75, c = 25

v_{1, 2} = \frac{- ( - 75 ) \pm ( - 75 ) ^{2} - 4 \cdot 25 \cdot 25}{2 \cdot 25}

v_{1, 2} = \frac{- ( - 75 ) \pm ( - 75 ) ^{2} - 4 \cdot 25 \cdot 25}{2 \cdot 25}

(- 75)^{2} - 4 \cdot 25 \cdot 25 = 255

(- 75)^{2} - 4 \cdot 25 \cdot 25

使用指数法则:

(- a)^{n} = a^{n},

若

n

是偶数

(- 75)^{2} = 7 5^{2}

= 7 5^{2} - 4 \cdot 25 \cdot 25

数字相乘:

4 \cdot 25 \cdot 25 = 2500

= 7 5^{2} - 2500

7 5^{2} = 5625

= 5625 - 2500

数字相减:

5625 - 2500 = 3125

= 3125

3125

质因数分解:

5^{5}

3125

3125

除以

53125 = 625 \cdot 5

= 5 \cdot 625

625

除以

5625 = 125 \cdot 5

= 5 \cdot 5 \cdot 125

125

除以

5125 = 25 \cdot 5

= 5 \cdot 5 \cdot 5 \cdot 25

25

除以

525 = 5 \cdot 5

= 5 \cdot 5 \cdot 5 \cdot 5 \cdot 5

5

是质数，因此无法进一步因数分解

= 5 \cdot 5 \cdot 5 \cdot 5 \cdot 5

= 5^{5}

= 5^{5}

使用指数法则:

a^{b + c} = a^{b} \cdot a^{c}

= 5^{4} \cdot 5

使用根式运算法则:

n ab = n a n b

= 5 5^{4}

使用根式运算法则:

n a^{m} = a^{\frac{m}{n}}

5^{4} = 5^{\frac{4}{2}} = 5^{2}

= 5^{2} 5

整理后得

= 255

v_{1, 2} = \frac{- ( - 75 ) \pm 25 5}{2 \cdot 25}

将解分隔开

v_{1} = \frac{- ( - 75 ) + 25 5}{2 \cdot 25}, v_{2} = \frac{- ( - 75 ) - 25 5}{2 \cdot 25}

v = \frac{- ( - 75 ) + 25 5}{2 \cdot 25} : \frac{3 + 5}{2}

\frac{- ( - 75 ) + 25 5}{2 \cdot 25}

使用法则

- (- a) = a

= \frac{75 + 25 5}{2 \cdot 25}

数字相乘:

2 \cdot 25 = 50

= \frac{75 + 25 5}{50}

分解

75 + 255 : 25 (3 + 5)

75 + 255

改写为

= 25 \cdot 3 + 255

因式分解出通项

25

= 25 (3 + 5)

= \frac{25 ( 3 + 5 )}{50}

约分:

25

= \frac{3 + 5}{2}

v = \frac{- ( - 75 ) - 25 5}{2 \cdot 25} : \frac{3 - 5}{2}

\frac{- ( - 75 ) - 25 5}{2 \cdot 25}

使用法则

- (- a) = a

= \frac{75 - 25 5}{2 \cdot 25}

数字相乘:

2 \cdot 25 = 50

= \frac{75 - 25 5}{50}

分解

75 - 255 : 25 (3 - 5)

75 - 255

改写为

= 25 \cdot 3 - 255

因式分解出通项

25

= 25 (3 - 5)

= \frac{25 ( 3 - 5 )}{50}

约分:

25

= \frac{3 - 5}{2}

二次方程组的解是:

v = \frac{3 + 5}{2}, v = \frac{3 - 5}{2}

v = \frac{3 + 5}{2}, v = \frac{3 - 5}{2}

验证解

找到无定义的点（奇点）:

v = 0

取

25 v + \frac{25}{v}

的分母，令其等于零

v = 0

以下点无定义

v = 0

将不在定义域的点与解相综合:

v = \frac{3 + 5}{2}, v = \frac{3 - 5}{2}

v = \frac{3 + 5}{2}, v = \frac{3 - 5}{2}

代回

v = u^{\frac{1}{50}}

，求解

u

解

u^{\frac{1}{50}} = \frac{3 + 5}{2} : u = \frac{( 3 + 5 ) ^{50}}{2 ^{50}}

u^{\frac{1}{50}} = \frac{3 + 5}{2}

对方程式两边

50

次方:

u = \frac{( 3 + 5 ) ^{50}}{2 ^{50}}

u^{\frac{1}{50}} = \frac{3 + 5}{2}

(u^{\frac{1}{50}})^{50} = (\frac{3 + 5}{2})^{50}

展开

(u^{\frac{1}{50}})^{50} : u

(u^{\frac{1}{50}})^{50}

使用指数法则:

(a^{b})^{c} = a^{b c}

= u^{\frac{1}{50} \cdot 50}

\frac{1}{50} \cdot 50 = 1

\frac{1}{50} \cdot 50

分式相乘:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 \cdot 50}{50}

约分:

50

= 1

= u

展开

(\frac{3 + 5}{2})^{50} : \frac{( 3 + 5 ) ^{50}}{2 ^{50}}

(\frac{3 + 5}{2})^{50}

使用指数法则:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{( 3 + 5 ) ^{50}}{2 ^{50}}

u = \frac{( 3 + 5 ) ^{50}}{2 ^{50}}

u = \frac{( 3 + 5 ) ^{50}}{2 ^{50}}

验证解:

u = \frac{( 3 + 5 ) ^{50}}{2 ^{50}}

真

将它们代入

u^{\frac{1}{50}} = \frac{3 + 5}{2}

检验解是否符合

去除与方程不符的解。

代入

u = \frac{( 3 + 5 ) ^{50}}{2 ^{50}} :

真

(\frac{( 3 + 5 ) ^{50}}{2 ^{50}})^{\frac{1}{50}} = \frac{3 + 5}{2}

(\frac{( 3 + 5 ) ^{50}}{2 ^{50}})^{\frac{1}{50}} = \frac{3 + 5}{2}

(\frac{( 3 + 5 ) ^{50}}{2 ^{50}})^{\frac{1}{50}}

使用根式运算法则:

n \frac{a}{b} = \frac{n a}{n b},

假定

a \geq 0, b \geq 0

= \frac{50 ( 3 + 5 ) ^{50}}{50 2 ^{50}}

使用根式运算法则:

n a^{n} = a,

假定

a \geq 0

50 2^{50} = 2

= \frac{50 ( 3 + 5 ) ^{50}}{2}

使用根式运算法则:

n a^{n} = a,

假定

a \geq 0

50 (3 + 5)^{50} = 3 + 5

= \frac{3 + 5}{2}

\frac{3 + 5}{2} = \frac{3 + 5}{2}

真

解是

u = \frac{( 3 + 5 ) ^{50}}{2 ^{50}}

解

u^{\frac{1}{50}} = \frac{3 - 5}{2} : u = \frac{( 3 - 5 ) ^{50}}{2 ^{50}}

u^{\frac{1}{50}} = \frac{3 - 5}{2}

对方程式两边

50

次方:

u = \frac{( 3 - 5 ) ^{50}}{2 ^{50}}

u^{\frac{1}{50}} = \frac{3 - 5}{2}

(u^{\frac{1}{50}})^{50} = (\frac{3 - 5}{2})^{50}

展开

(u^{\frac{1}{50}})^{50} : u

(u^{\frac{1}{50}})^{50}

使用指数法则:

(a^{b})^{c} = a^{b c}

= u^{\frac{1}{50} \cdot 50}

\frac{1}{50} \cdot 50 = 1

\frac{1}{50} \cdot 50

分式相乘:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 \cdot 50}{50}

约分:

50

= 1

= u

展开

(\frac{3 - 5}{2})^{50} : \frac{( 3 - 5 ) ^{50}}{2 ^{50}}

(\frac{3 - 5}{2})^{50}

使用指数法则:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{( 3 - 5 ) ^{50}}{2 ^{50}}

u = \frac{( 3 - 5 ) ^{50}}{2 ^{50}}

u = \frac{( 3 - 5 ) ^{50}}{2 ^{50}}

验证解:

u = \frac{( 3 - 5 ) ^{50}}{2 ^{50}}

真

将它们代入

u^{\frac{1}{50}} = \frac{3 - 5}{2}

检验解是否符合

去除与方程不符的解。

代入

u = \frac{( 3 - 5 ) ^{50}}{2 ^{50}} :

真

(\frac{( 3 - 5 ) ^{50}}{2 ^{50}})^{\frac{1}{50}} = \frac{3 - 5}{2}

(\frac{( 3 - 5 ) ^{50}}{2 ^{50}})^{\frac{1}{50}} = \frac{3 - 5}{2}

(\frac{( 3 - 5 ) ^{50}}{2 ^{50}})^{\frac{1}{50}}

使用根式运算法则:

n \frac{a}{b} = \frac{n a}{n b},

假定

a \geq 0, b \geq 0

= \frac{50 ( 3 - 5 ) ^{50}}{50 2 ^{50}}

使用根式运算法则:

n a^{n} = a,

假定

a \geq 0

50 2^{50} = 2

= \frac{50 ( 3 - 5 ) ^{50}}{2}

使用根式运算法则:

n a^{n} = a,

假定

a \geq 0

50 (3 - 5)^{50} = 3 - 5

= \frac{3 - 5}{2}

\frac{3 - 5}{2} = \frac{3 - 5}{2}

真

解是

u = \frac{( 3 - 5 ) ^{50}}{2 ^{50}}

u = \frac{( 3 + 5 ) ^{50}}{2 ^{50}}, u = \frac{( 3 - 5 ) ^{50}}{2 ^{50}}

验证解:

u = \frac{( 3 + 5 ) ^{50}}{2 ^{50}}

真

, u = \frac{( 3 - 5 ) ^{50}}{2 ^{50}}

真

将它们代入

50 \frac{u ^{0.02} + u ^{- 0.02}}{2} = 75

检验解是否符合

去除与方程不符的解。

代入

u = \frac{( 3 + 5 ) ^{50}}{2 ^{50}} :

真

50 \cdot \frac{( \frac{( 3 + 5 ) ^{50}}{2 ^{50}} ) ^{0.02} + ( \frac{( 3 + 5 ) ^{50}}{2 ^{50}} ) ^{- 0.02}}{2} = 75

50 \cdot \frac{( \frac{( 3 + 5 ) ^{50}}{2 ^{50}} ) ^{0.02} + ( \frac{( 3 + 5 ) ^{50}}{2 ^{50}} ) ^{- 0.02}}{2} = 75

50 \cdot \frac{( \frac{( 3 + 5 ) ^{50}}{2 ^{50}} ) ^{0.02} + ( \frac{( 3 + 5 ) ^{50}}{2 ^{50}} ) ^{- 0.02}}{2}

\frac{( \frac{( 3 + 5 ) ^{50}}{2 ^{50}} ) ^{0.02} + ( \frac{( 3 + 5 ) ^{50}}{2 ^{50}} ) ^{- 0.02}}{2} = \frac{3}{2}

\frac{( \frac{( 3 + 5 ) ^{50}}{2 ^{50}} ) ^{0.02} + ( \frac{( 3 + 5 ) ^{50}}{2 ^{50}} ) ^{- 0.02}}{2}

(\frac{( 3 + 5 ) ^{50}}{2 ^{50}})^{0.02} = 2.61803 \dots

(\frac{( 3 + 5 ) ^{50}}{2 ^{50}})^{0.02}

\frac{( 3 + 5 ) ^{50}}{2 ^{50}} = 7.92071 E 20

\frac{( 3 + 5 ) ^{50}}{2 ^{50}}

转换为小数形式

2^{50} = 1.1259 E 15

= \frac{( 3 + 5 ) ^{50}}{1.1259 E 15}

转换为小数形式

(3 + 5)^{50} = 8.91792 E 35

= \frac{8.91792 E 35}{1.1259 E 15}

数字相除:

\frac{8.91792 E 35}{1.1259 E 15} = 7.92071 E 20

= 7.92071 E 20

= 7.92071 E 2 0^{0.02}

7.92071 E 2 0^{0.02} = 2.61803 \dots

= 2.61803 \dots

(\frac{( 3 + 5 ) ^{50}}{2 ^{50}})^{- 0.02} = 0.38196 \dots

(\frac{( 3 + 5 ) ^{50}}{2 ^{50}})^{- 0.02}

\frac{( 3 + 5 ) ^{50}}{2 ^{50}} = 7.92071 E 20

\frac{( 3 + 5 ) ^{50}}{2 ^{50}}

转换为小数形式

2^{50} = 1.1259 E 15

= \frac{( 3 + 5 ) ^{50}}{1.1259 E 15}

转换为小数形式

(3 + 5)^{50} = 8.91792 E 35

= \frac{8.91792 E 35}{1.1259 E 15}

数字相除:

\frac{8.91792 E 35}{1.1259 E 15} = 7.92071 E 20

= 7.92071 E 20

= 7.92071 E 2 0^{- 0.02}

7.92071 E 2 0^{- 0.02} = 0.38196 \dots

= 0.38196 \dots

= \frac{2.61803 \dots + 0.38196 \dots}{2}

数字相加:

2.61803 \dots + 0.38196 \dots = 3

= \frac{3}{2}

= 50 \cdot \frac{3}{2}

分式相乘:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{3 \cdot 50}{2}

数字相乘:

3 \cdot 50 = 150

= \frac{150}{2}

数字相除:

\frac{150}{2} = 75

= 75

75 = 75

真

代入

u = \frac{( 3 - 5 ) ^{50}}{2 ^{50}} :

真

50 \cdot \frac{( \frac{( 3 - 5 ) ^{50}}{2 ^{50}} ) ^{0.02} + ( \frac{( 3 - 5 ) ^{50}}{2 ^{50}} ) ^{- 0.02}}{2} = 75

50 \cdot \frac{( \frac{( 3 - 5 ) ^{50}}{2 ^{50}} ) ^{0.02} + ( \frac{( 3 - 5 ) ^{50}}{2 ^{50}} ) ^{- 0.02}}{2} = 75

50 \cdot \frac{( \frac{( 3 - 5 ) ^{50}}{2 ^{50}} ) ^{0.02} + ( \frac{( 3 - 5 ) ^{50}}{2 ^{50}} ) ^{- 0.02}}{2}

\frac{( \frac{( 3 - 5 ) ^{50}}{2 ^{50}} ) ^{0.02} + ( \frac{( 3 - 5 ) ^{50}}{2 ^{50}} ) ^{- 0.02}}{2} = \frac{3}{2}

\frac{( \frac{( 3 - 5 ) ^{50}}{2 ^{50}} ) ^{0.02} + ( \frac{( 3 - 5 ) ^{50}}{2 ^{50}} ) ^{- 0.02}}{2}

(\frac{( 3 - 5 ) ^{50}}{2 ^{50}})^{0.02} = 0.38196 \dots

(\frac{( 3 - 5 ) ^{50}}{2 ^{50}})^{0.02}

\frac{( 3 - 5 ) ^{50}}{2 ^{50}} = 1.26251 E - 21

\frac{( 3 - 5 ) ^{50}}{2 ^{50}}

转换为小数形式

2^{50} = 1.1259 E 15

= \frac{( 3 - 5 ) ^{50}}{1.1259 E 15}

转换为小数形式

(3 - 5)^{50} = 1.42146 E - 6

= \frac{1.42146 E - 6}{1.1259 E 15}

数字相除:

\frac{1.42146 E - 6}{1.1259 E 15} = 1.26251 E - 21

= 1.26251 E - 21

= 1.26251 E - 2 1^{0.02}

1.26251 E - 2 1^{0.02} = 0.38196 \dots

= 0.38196 \dots

(\frac{( 3 - 5 ) ^{50}}{2 ^{50}})^{- 0.02} = 2.61803 \dots

(\frac{( 3 - 5 ) ^{50}}{2 ^{50}})^{- 0.02}

\frac{( 3 - 5 ) ^{50}}{2 ^{50}} = 1.26251 E - 21

\frac{( 3 - 5 ) ^{50}}{2 ^{50}}

转换为小数形式

2^{50} = 1.1259 E 15

= \frac{( 3 - 5 ) ^{50}}{1.1259 E 15}

转换为小数形式

(3 - 5)^{50} = 1.42146 E - 6

= \frac{1.42146 E - 6}{1.1259 E 15}

数字相除:

\frac{1.42146 E - 6}{1.1259 E 15} = 1.26251 E - 21

= 1.26251 E - 21

= 1.26251 E - 2 1^{- 0.02}

使用指数法则:

a^{- b} = \frac{1}{a ^{b}}

= \frac{1}{1.26251 E - 2 1 ^{0.02}}

1.26251 E - 2 1^{0.02} = 0.38196 \dots

= \frac{1}{0.38196 \dots}

数字相除:

\frac{1}{0.38196 \dots} = 2.61803 \dots

= 2.61803 \dots

= \frac{0.38196 \dots + 2.61803 \dots}{2}

数字相加:

0.38196 \dots + 2.61803 \dots = 3

= \frac{3}{2}

= 50 \cdot \frac{3}{2}

分式相乘:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{3 \cdot 50}{2}

数字相乘:

3 \cdot 50 = 150

= \frac{150}{2}

数字相除:

\frac{150}{2} = 75

= 75

75 = 75

真

解为

u = \frac{( 3 + 5 ) ^{50}}{2 ^{50}}, u = \frac{( 3 - 5 ) ^{50}}{2 ^{50}}

u = \frac{( 3 + 5 ) ^{50}}{2 ^{50}}, u = \frac{( 3 - 5 ) ^{50}}{2 ^{50}}

代回

u = e^{x}

，求解

x

解

e^{x} = \frac{( 3 + 5 ) ^{50}}{2 ^{50}} : x = 50 ln (\frac{3 + 5}{2})

e^{x} = \frac{( 3 + 5 ) ^{50}}{2 ^{50}}

使用指数运算法则

e^{x} = \frac{( 3 + 5 ) ^{50}}{2 ^{50}}

使用指数法则:

\frac{1}{a ^{b}} = a^{- b}

\frac{1}{2 ^{50}} = 2^{- 50}

e^{x} = (3 + 5)^{50} \cdot 2^{- 50}

若

f (x) = g (x)

，则

ln (f (x)) = ln (g (x))

ln (e^{x}) = ln ((3 + 5)^{50} \cdot 2^{- 50})

使用对数计算法则:

ln (e^{a}) = a

ln (e^{x}) = x

x = ln ((3 + 5)^{50} \cdot 2^{- 50})

化简

ln ((3 + 5)^{50} \cdot 2^{- 50}) : 50 ln (\frac{3 + 5}{2})

ln ((3 + 5)^{50} \cdot 2^{- 50})

乘

(3 + 5)^{50} \cdot 2^{- 50} : \frac{( 3 + 5 ) ^{50}}{2 ^{50}}

(3 + 5)^{50} \cdot 2^{- 50}

使用指数法则:

a^{- b} = \frac{1}{a ^{b}}

2^{- 50} = \frac{1}{2 ^{50}}

= \frac{1}{2 ^{50}} (3 + 5)^{50}

分式相乘:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 \cdot ( 3 + 5 ) ^{50}}{2 ^{50}}

乘以:

1 \cdot (3 + 5)^{50} = (3 + 5)^{50}

= \frac{( 3 + 5 ) ^{50}}{2 ^{50}}

= ln (\frac{( 3 + 5 ) ^{50}}{2 ^{50}})

合并相同指数项 :

\frac{x ^{n}}{y ^{n}} = (\frac{x}{y})^{n}

= ln (\frac{3 + 5}{2})^{50}

使用对数运算法则:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x),

假定

x \geq 0

= 50 ln (\frac{3 + 5}{2})

x = 50 ln (\frac{3 + 5}{2})

x = 50 ln (\frac{3 + 5}{2})

解

e^{x} = \frac{( 3 - 5 ) ^{50}}{2 ^{50}} : x \in R

无解

e^{x} = \frac{( 3 - 5 ) ^{50}}{2 ^{50}}

使用指数运算法则

e^{x} = \frac{( 3 - 5 ) ^{50}}{2 ^{50}}

使用指数法则:

\frac{1}{a ^{b}} = a^{- b}

\frac{1}{2 ^{50}} = 2^{- 50}

e^{x} = (3 - 5)^{50} \cdot 2^{- 50}

e^{x} = (3 - 5)^{50} \cdot 2^{- 50}

a^{f (x)}

对于

x

不能为零或负值

\in R

x \in R 无解

x = 50 ln (\frac{3 + 5}{2})

x = 50 ln (\frac{3 + 5}{2})

作图

流行的例子

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