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人気のある代数 >

log_{2}(x)-2log_{x}(3)=0

解

lo g_{2} (x) - 2 lo g_{x} (3) = 0

解

x = 2^{2 l o g_{2} (3)}, x = \frac{1}{2 ^{2 l o g_{2} (3)}}

+1

十進法表記

x = 3.43528 \dots, x = 0.29109 \dots

解答ステップ

lo g_{2} (x) - 2 lo g_{x} (3) = 0

対数の規則を適用する

lo g_{2} (x) - \frac{2 lo g _{2} ( 3 )}{lo g _{2} ( x )} = 0

equationを以下で書き換える:

lo g_{2} (x) = u

u - \frac{2 lo g _{2} ( 3 )}{u} = 0

解く

u - \frac{2 lo g _{2} ( 3 )}{u} = 0 : u = 2 lo g_{2} (3), u = - 2 lo g_{2} (3)

u = 2 lo g_{2} (3), u = - 2 lo g_{2} (3)

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) = 2 lo g_{2} (3) : x = 2^{2 l o g_{2} (3)}

解く

lo g_{2} (x) = - 2 lo g_{2} (3) : x = \frac{1}{2 ^{2 l o g_{2} (3)}}

x = 2^{2 l o g_{2} (3)}, x = \frac{1}{2 ^{2 l o g_{2} (3)}}

解を検算する:

x = 2^{2 l o g_{2} (3)}

真

, x = \frac{1}{2 ^{2 l o g_{2} (3)}}

真

解答は

x = 2^{2 l o g_{2} (3)}, x = \frac{1}{2 ^{2 l o g_{2} (3)}}

グラフ

人気の例

ln (5 x - 6) = 3

log_{1/2}(-x+4)=-2

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

log_{2}(x+1)+log_{2}(x+7)=3

lo g_{2} (x + 1) + lo g_{2} (x + 7) = 3

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

2 = lo g_{3} (x)