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人気のある代数 >

8log_{10}(n)-n=0

解

8 lo g_{10} (n) - n = 0

解

n = - \frac{8 W _{- 1} ( - \frac{l n ( 10 )}{8} )}{ln ( 10 )}, n = - \frac{8 W _{0} ( - \frac{l n ( 10 )}{8} )}{ln ( 10 )}

+1

十進法表記

n = 6.50709 \dots, n = 1.57231 \dots

解答ステップ

8 lo g_{10} (n) - n = 0

n

を右側に移動します

8 lo g_{10} (n) = n

以下で両辺を割る

8

lo g_{10} (n) = \frac{n}{8}

f (x) = g (x)

ならば,

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

1 0^{l o g_{10} (n)} = 1 0^{\frac{n}{8}}

簡素化

1 0^{l o g_{10} (n)} : n

n = 1 0^{\frac{n}{8}}

解く

n = 1 0^{\frac{n}{8}} : n = - \frac{8 W _{- 1} ( - \frac{l n ( 10 )}{8} )}{ln ( 10 )}, n = - \frac{8 W _{0} ( - \frac{l n ( 10 )}{8} )}{ln ( 10 )}

n = - \frac{8 W _{- 1} ( - \frac{l n ( 10 )}{8} )}{ln ( 10 )}, n = - \frac{8 W _{0} ( - \frac{l n ( 10 )}{8} )}{ln ( 10 )}

解を検算する:

n = - \frac{8 W _{- 1} ( - \frac{l n ( 10 )}{8} )}{ln ( 10 )}

真

, n = - \frac{8 W _{0} ( - \frac{l n ( 10 )}{8} )}{ln ( 10 )}

真

解答は

n = - \frac{8 W _{- 1} ( - \frac{l n ( 10 )}{8} )}{ln ( 10 )}, n = - \frac{8 W _{0} ( - \frac{l n ( 10 )}{8} )}{ln ( 10 )}

グラフ

人気の例

log_{x}(100)=140

lo g_{x} (100) = 140

log_{-2x-8}(2x^2+6x-20)=2

lo g_{- 2 x - 8} (2 x^{2} + 6 x - 20) = 2

log_{12}(1+r/(100))=3

lo g_{12} (1 + \frac{r}{100}) = 3

log_{5}(x)-log_{5}(x-1)=1

lo g_{5} (x) - lo g_{5} (x - 1) = 1

log_{6}(x+4)=1-log_{6}(x+3)

lo g_{6} (x + 4) = 1 - lo g_{6} (x + 3)