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人気のある代数 >

ln(x)+3= 4/(ln(x))

解

ln (x) + 3 = \frac{4}{ln ( x )}

解

x = e, x = \frac{1}{e ^{4}}

+1

十進法表記

x = 2.71828 \dots, x = 0.01831 \dots

解答ステップ

ln (x) + 3 = \frac{4}{ln ( x )}

以下で両辺を乗じる:

ln (x)

ln (x) ln (x) + 3 ln (x) = \frac{4}{ln ( x )} ln (x)

簡素化

ln (x) ln (x) + 3 ln (x) : ln^{2} (x) + 3 ln (x)

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

equationを以下で書き換える:

ln (x) = u

u^{2} + 3 u = 4

解く

u^{2} + 3 u = 4 : u = 1, u = - 4

u = 1, u = - 4

再び

u = ln (x)

に置き換えて以下を解く:

x

解く

ln (x) = 1 : x = e

解く

ln (x) = - 4 : x = \frac{1}{e ^{4}}

x = e, x = \frac{1}{e ^{4}}

解を検算する:

x = e

真

, x = \frac{1}{e ^{4}}

真

解答は

x = e, x = \frac{1}{e ^{4}}

グラフ

人気の例

log_{7}(9-x)=3log_{7}(2)

lo g_{7} (9 - x) = 3 lo g_{7} (2)

solvefor x,log_{10}(x)=-2

so l v e f or x, lo g_{10} (x) = - 2

log_{10}(x)=97261

lo g_{10} (x) = 97261

ln(x-2)=ln(12)-ln(x+2)

ln (x - 2) = ln (12) - ln (x + 2)

(log_{e}(x-1))^2=4

(lo g_{e} (x - 1))^{2} = 4