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人気のある代数 >

w/(log_{2)(w+1)}=3

解

\frac{w}{lo g _{2} ( w + 1 )} = 3

解

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

+1

十進法表記

w = 10.61301 \dots

解答ステップ

\frac{w}{lo g _{2} ( w + 1 )} = 3

以下で両辺を乗じる:

lo g_{2} (w + 1)

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

辺を交換する

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

以下で両辺を割る

3

lo g_{2} (w + 1) = \frac{w}{3}

f (x) = g (x)

ならば,

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

2^{l o g_{2} (w + 1)} = 2^{\frac{w}{3}}

簡素化

2^{l o g_{2} (w + 1)} : w + 1

w + 1 = 2^{\frac{w}{3}}

解く

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

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

解を検算する:

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

真

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

偽

解は

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

グラフ

人気の例

log_{10}(n)=1000

lo g_{10} (n) = 1000

0.47 = ln (y)

ln(2x)-3ln(x^3)=0

ln (2 x) - 3 ln (x^{3}) = 0

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

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

ln(4x)+ln(2x)=3

ln (4 x) + ln (2 x) = 3