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人気のある代数 >

3^x+3^{-x}=5

解

3^{x} + 3^{- x} = 5

解

x = \frac{ln ( \frac{5 + 21}{2} )}{ln ( 3 )}, x = \frac{ln ( \frac{5 - 21}{2} )}{ln ( 3 )}

+1

十進法表記

x = 1.42616 \dots, x = - 1.42616 \dots

解答ステップ

3^{x} + 3^{- x} = 5

指数の規則を適用する

3^{x} + (3^{x})^{- 1} = 5

equationを以下で書き換える:

3^{x} = u

u + (u)^{- 1} = 5

解く

u + u^{- 1} = 5 : u = \frac{5 + 21}{2}, u = \frac{5 - 21}{2}

u = \frac{5 + 21}{2}, u = \frac{5 - 21}{2}

再び

u = 3^{x}

に置き換えて以下を解く:

x

解く

3^{x} = \frac{5 + 21}{2} : x = \frac{ln ( \frac{5 + 21}{2} )}{ln ( 3 )}

解く

3^{x} = \frac{5 - 21}{2} : x = \frac{ln ( \frac{5 - 21}{2} )}{ln ( 3 )}

x = \frac{ln ( \frac{5 + 21}{2} )}{ln ( 3 )}, x = \frac{ln ( \frac{5 - 21}{2} )}{ln ( 3 )}

グラフ

人気の例

ln(e^x-3e^{-x})=ln(2)

ln (e^{x} - 3 e^{- x}) = ln (2)

4^{x+1}=2^{x-1}

4^{x + 1} = 2^{x - 1}

3^{2 x - 1} = 7^{x}

(7^{x})^{x - 3} = 1

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

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