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人気のある代数 >

ln(4x)-3ln(x^2)=ln^2(x)

解

ln (4 x) - 3 ln (x^{2}) = ln^{2} (x)

解

x = e^{\frac{- 5 + 25 + 8 l n ( 2 )}{2}}, x = e^{\frac{- 5 - 25 + 8 l n ( 2 )}{2}}

+1

十進法表記

x = 1.30132 \dots, x = 0.00517 \dots

解答ステップ

ln (4 x) - 3 ln (x^{2}) = ln^{2} (x)

対数の規則を適用する

ln (4) + ln (x) - 3 \cdot 2 ln (x) = ln^{2} (x)

equationを以下で書き換える:

ln (x) = u

ln (4) + u - 3 \cdot 2 u = u^{2}

解く

ln (4) + u - 3 \cdot 2 u = u^{2} : u = \frac{- 5 + 25 + 8 ln ( 2 )}{2}, u = \frac{- 5 - 25 + 8 ln ( 2 )}{2}

u = \frac{- 5 + 25 + 8 ln ( 2 )}{2}, u = \frac{- 5 - 25 + 8 ln ( 2 )}{2}

再び

u = ln (x)

に置き換えて以下を解く:

x

解く

ln (x) = \frac{- 5 + 25 + 8 ln ( 2 )}{2} : x = e^{\frac{- 5 + 25 + 8 l n ( 2 )}{2}}

解く

ln (x) = \frac{- 5 - 25 + 8 ln ( 2 )}{2} : x = e^{\frac{- 5 - 25 + 8 l n ( 2 )}{2}}

x = e^{\frac{- 5 + 25 + 8 l n ( 2 )}{2}}, x = e^{\frac{- 5 - 25 + 8 l n ( 2 )}{2}}

解を検算する:

x = e^{\frac{- 5 + 25 + 8 l n ( 2 )}{2}}

真

, x = e^{\frac{- 5 - 25 + 8 l n ( 2 )}{2}}

真

解答は

x = e^{\frac{- 5 + 25 + 8 l n ( 2 )}{2}}, x = e^{\frac{- 5 - 25 + 8 l n ( 2 )}{2}}

グラフ

人気の例

(ln(x))^3=7ln(x)

(ln (x))^{3} = 7 ln (x)

log_{4}(100-3x)=23219

lo g_{4} (100 - 3 x) = 23219

6 = lo g_{10} (x)

solvefor x,-5log_{3}(2x)=-5

so l v e f or x, - 5 lo g_{3} (2 x) = - 5

1+log_{1/2}(x)=0

1 + lo g_{\frac{1}{2}} (x) = 0