ja

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

人気のある代数 >

3^x-(sqrt(3))^{x+4}+20=0

解

3^{x} - (3)^{x + 4} + 20 = 0

解

x = \frac{2 ln ( 5 )}{ln ( 3 )}, x = \frac{4 ln ( 2 )}{ln ( 3 )}

+1

十進法表記

x = 2.92994 \dots, x = 2.52371 \dots

解答ステップ

3^{x} - (3)^{x + 4} + 20 = 0

指数の規則を適用する

3^{x} - 3^{x} \cdot 3^{2} + 20 = 0

equationを以下で書き換える:

3^{x} = u

u - u \cdot 3^{2} + 20 = 0

解く

u - u \cdot 3^{2} + 20 = 0 : u = 25, u = 16

u = 25, u = 16

再び

u = 3^{x}

に置き換えて以下を解く:

x

解く

3^{x} = 25 : x = \frac{2 ln ( 5 )}{ln ( 3 )}

解く

3^{x} = 16 : x = \frac{4 ln ( 2 )}{ln ( 3 )}

x = \frac{2 ln ( 5 )}{ln ( 3 )}, x = \frac{4 ln ( 2 )}{ln ( 3 )}

グラフ

人気の例

18^x-8*6^x-9*2^x=0

1 8^{x} - 8 \cdot 6^{x} - 9 \cdot 2^{x} = 0

2^{x} = 3^{x + 1}

2^{x} \cdot 2^{4} = 2^{2 x}

3^{x - 1} = 2^{x}

5^{2x^2-3x-2}=1

5^{2 x^{2} - 3 x - 2} = 1