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人気のある代数 >

ln^2(x-6)+ln^2(m+1)=3

解

ln^{2} (x - 6) + ln^{2} (m + 1) = 3

解

x = e^{3 - l n^{2} (m + 1)} + 6 {\frac{1}{e ^{3}} - 1 \leq m \leq e^{3} - 1}, x = e^{- 3 - l n^{2} (m + 1)} + 6 {\frac{1}{e ^{3}} - 1 \leq m \leq e^{3} - 1}

解答ステップ

ln^{2} (x - 6) + ln^{2} (m + 1) = 3

equationを以下で書き換える:

ln (x - 6) = u

u^{2} + ln^{2} (m + 1) = 3

解く

u^{2} + ln^{2} (m + 1) = 3 : u = 3 - ln^{2} (m + 1), u = - 3 - ln^{2} (m + 1)

u = 3 - ln^{2} (m + 1), u = - 3 - ln^{2} (m + 1)

再び

u = ln (x - 6)

に置き換えて以下を解く:

x

解く

ln (x - 6) = 3 - ln^{2} (m + 1) : x = e^{3 - l n^{2} (m + 1)} + 6

解く

ln (x - 6) = - 3 - ln^{2} (m + 1) : x = e^{- 3 - l n^{2} (m + 1)} + 6

x = e^{3 - l n^{2} (m + 1)} + 6, x = e^{- 3 - l n^{2} (m + 1)} + 6

解を検算する:

x = e^{3 - l n^{2} (m + 1)} + 6 {\frac{1}{e ^{3}} - 1 \leq m \leq e^{3} - 1}, x = e^{- 3 - l n^{2} (m + 1)} + 6 {\frac{1}{e ^{3}} - 1 \leq m \leq e^{3} - 1}

解答は

x = e^{3 - l n^{2} (m + 1)} + 6 {\frac{1}{e ^{3}} - 1 \leq m \leq e^{3} - 1}, x = e^{- 3 - l n^{2} (m + 1)} + 6 {\frac{1}{e ^{3}} - 1 \leq m \leq e^{3} - 1}

グラフ

人気の例

log_{10}(x*10^{-3})=2.85

lo g_{10} (x \cdot 1 0^{- 3}) = 2.85

x (1 - ln (x)) = 0

log_{2}(x)=3.6*10^{13}

lo g_{2} (x) = 3.6 \cdot 1 0^{13}

5= 1/3 log_{10}(x)+3

5 = \frac{1}{3} lo g_{10} (x) + 3

log_{x}(16/625)=4

lo g_{x} (\frac{16}{625}) = 4