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人気のある代数 >

2log_{10}(9-2x)=(3-x)

解

2 lo g_{10} (9 - 2 x) = (3 - x)

解

x = \frac{2 W _{- 1} ( - \frac{l n ( 10 )}{4 e ^{\frac{3 l n ( 10 )}{4}}} )}{ln ( 10 )} + \frac{9}{2}, x = \frac{2 W _{0} ( - \frac{l n ( 10 )}{4 e ^{\frac{3 l n ( 10 )}{4}}} )}{ln ( 10 )} + \frac{9}{2}

+1

十進法表記

x = 1.42116 \dots, x = 4.40026 \dots

解答ステップ

2 lo g_{10} (9 - 2 x) = (3 - x)

以下で両辺を割る

2

lo g_{10} (9 - 2 x) = \frac{3 - x}{2}

f (x) = g (x)

ならば,

a^{f (x)} = a^{g (x)}

1 0^{l o g_{10} (9 - 2 x)} = 1 0^{\frac{3 - x}{2}}

簡素化

1 0^{l o g_{10} (9 - 2 x)} : 9 - 2 x

9 - 2 x = 1 0^{\frac{3 - x}{2}}

解く

9 - 2 x = 1 0^{\frac{3 - x}{2}} : x = \frac{2 W _{- 1} ( - \frac{l n ( 10 )}{4 e ^{\frac{3 l n ( 10 )}{4}}} )}{ln ( 10 )} + \frac{9}{2}, x = \frac{2 W _{0} ( - \frac{l n ( 10 )}{4 e ^{\frac{3 l n ( 10 )}{4}}} )}{ln ( 10 )} + \frac{9}{2}

x = \frac{2 W _{- 1} ( - \frac{l n ( 10 )}{4 e ^{\frac{3 l n ( 10 )}{4}}} )}{ln ( 10 )} + \frac{9}{2}, x = \frac{2 W _{0} ( - \frac{l n ( 10 )}{4 e ^{\frac{3 l n ( 10 )}{4}}} )}{ln ( 10 )} + \frac{9}{2}

解を検算する:

x = \frac{2 W _{- 1} ( - \frac{l n ( 10 )}{4 e ^{\frac{3 l n ( 10 )}{4}}} )}{ln ( 10 )} + \frac{9}{2}

真

, x = \frac{2 W _{0} ( - \frac{l n ( 10 )}{4 e ^{\frac{3 l n ( 10 )}{4}}} )}{ln ( 10 )} + \frac{9}{2}

真

解答は

x = \frac{2 W _{- 1} ( - \frac{l n ( 10 )}{4 e ^{\frac{3 l n ( 10 )}{4}}} )}{ln ( 10 )} + \frac{9}{2}, x = \frac{2 W _{0} ( - \frac{l n ( 10 )}{4 e ^{\frac{3 l n ( 10 )}{4}}} )}{ln ( 10 )} + \frac{9}{2}

グラフ

人気の例

log_{10}(5x+1)=2+log_{10}(2x-3)

lo g_{10} (5 x + 1) = 2 + lo g_{10} (2 x - 3)

4log_{2}(2x)=36

4 lo g_{2} (2 x) = 36

log_{10}(n)=-0.35

lo g_{10} (n) = - 0.35

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

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

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

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