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人気のある代数 >

(log_{2}(x))^2+2*log_{2}(sqrt(x))-2=0

解

(lo g_{2} (x))^{2} + 2 \cdot lo g_{2} (x) - 2 = 0

解

x = 2, x = \frac{1}{4}

+1

十進法表記

x = 2, x = 0.25

解答ステップ

(lo g_{2} (x))^{2} + 2 lo g_{2} (x) - 2 = 0

対数の規則を適用する

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

equationを以下で書き換える:

lo g_{2} (x) = u

(u)^{2} + 2 \cdot \frac{1}{2} u - 2 = 0

解く

u^{2} + 2 \cdot \frac{1}{2} u - 2 = 0 : u = 1, u = - 2

u = 1, u = - 2

再び

u = lo g_{2} (x)

に置き換えて以下を解く:

x

解く

lo g_{2} (x) = 1 : x = 2

解く

lo g_{2} (x) = - 2 : x = \frac{1}{4}

x = 2, x = \frac{1}{4}

解を検算する:

x = 2

真

, x = \frac{1}{4}

真

解答は

x = 2, x = \frac{1}{4}

グラフ

人気の例

(log_{10}(10x))2-4log_{10}(10x)-5=0

(lo g_{10} (10 x)) 2 - 4 lo g_{10} (10 x) - 5 = 0

6log_{10}(a)+6log_{10}(a-9)=2

6 lo g_{10} (a) + 6 lo g_{10} (a - 9) = 2

ln(x-1)-ln(x+2)=ln(2)

ln (x - 1) - ln (x + 2) = ln (2)

alog_{2}(3.5)=log_{27}(-log_{22}(x))

a lo g_{2} (3.5) = lo g_{27} (- lo g_{22} (x))

x-7+log_{2}(x+8)=-5

x - 7 + lo g_{2} (x + 8) = - 5