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人気のある代数 >

3log_{10}(2x+4)=x+1

解

3 lo g_{10} (2 x + 4) = x + 1

解

x = - \frac{3 W _{- 1} ( - \frac{l n ( 10 )}{6 e ^{\frac{l n ( 10 )}{3}}} )}{ln ( 10 )} - 2, x = - \frac{3 W _{0} ( - \frac{l n ( 10 )}{6 e ^{\frac{l n ( 10 )}{3}}} )}{ln ( 10 )} - 2

+1

十進法表記

x = 1.55596 \dots, x = - 1.71008 \dots

解答ステップ

3 lo g_{10} (2 x + 4) = x + 1

以下で両辺を割る

3

lo g_{10} (2 x + 4) = \frac{x + 1}{3}

f (x) = g (x)

ならば,

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

1 0^{l o g_{10} (2 x + 4)} = 1 0^{\frac{x + 1}{3}}

簡素化

1 0^{l o g_{10} (2 x + 4)} : 2 x + 4

2 x + 4 = 1 0^{\frac{x + 1}{3}}

解く

2 x + 4 = 1 0^{\frac{x + 1}{3}} : x = - \frac{3 W _{- 1} ( - \frac{l n ( 10 )}{6 e ^{\frac{l n ( 10 )}{3}}} )}{ln ( 10 )} - 2, x = - \frac{3 W _{0} ( - \frac{l n ( 10 )}{6 e ^{\frac{l n ( 10 )}{3}}} )}{ln ( 10 )} - 2

x = - \frac{3 W _{- 1} ( - \frac{l n ( 10 )}{6 e ^{\frac{l n ( 10 )}{3}}} )}{ln ( 10 )} - 2, x = - \frac{3 W _{0} ( - \frac{l n ( 10 )}{6 e ^{\frac{l n ( 10 )}{3}}} )}{ln ( 10 )} - 2

解を検算する:

x = - \frac{3 W _{- 1} ( - \frac{l n ( 10 )}{6 e ^{\frac{l n ( 10 )}{3}}} )}{ln ( 10 )} - 2

真

, x = - \frac{3 W _{0} ( - \frac{l n ( 10 )}{6 e ^{\frac{l n ( 10 )}{3}}} )}{ln ( 10 )} - 2

真

解答は

x = - \frac{3 W _{- 1} ( - \frac{l n ( 10 )}{6 e ^{\frac{l n ( 10 )}{3}}} )}{ln ( 10 )} - 2, x = - \frac{3 W _{0} ( - \frac{l n ( 10 )}{6 e ^{\frac{l n ( 10 )}{3}}} )}{ln ( 10 )} - 2

グラフ

人気の例

log_{x}(9/4)=-2

lo g_{x} (\frac{9}{4}) = - 2

solvefor x,y=ln(x-1)

so l v e f or x, y = ln (x - 1)

4 ln (6 x) = - 4

lo g_{x} (\frac{9}{4}) = 2

3log_{10}(4-x)=1-x

3 lo g_{10} (4 - x) = 1 - x