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人気のある代数 >

3^{2x}-10× 3^x+21=0

解

3^{2 x} - 10 \cdot 3^{x} + 21 = 0

解

x = \frac{ln ( 7 )}{ln ( 3 )}, x = 1

+1

十進法表記

x = 1.77124 \dots, x = 1

解答ステップ

3^{2 x} - 10 \cdot 3^{x} + 21 = 0

指数の規則を適用する

(3^{x})^{2} - 10 \cdot 3^{x} + 21 = 0

equationを以下で書き換える:

3^{x} = u

(u)^{2} - 10 u + 21 = 0

解く

u^{2} - 10 u + 21 = 0 : u = 7, u = 3

u = 7, u = 3

再び

u = 3^{x}

に置き換えて以下を解く:

x

解く

3^{x} = 7 : x = \frac{ln ( 7 )}{ln ( 3 )}

解く

3^{x} = 3 : x = 1

x = \frac{ln ( 7 )}{ln ( 3 )}, x = 1

グラフ

人気の例

9 \cdot 2^{2 x} = 1

\sqrt[3]{(2^7-2^x)/(2^x-2)}=2

3 \frac{2 ^{7} - 2 ^{x}}{2 ^{x} - 2} = 2

solvefor x,2^x=16

so l v e f or x, 2^{x} = 16

3^{2x}+3^{x+1}-54=0

3^{2 x} + 3^{x + 1} - 54 = 0

8^{x} = 70