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人気のある代数 >

5000*log_{2}(n)=n

解

5000 \cdot lo g_{2} (n) = n

解

n = - \frac{5000 W _{- 1} ( - \frac{l n ( 2 )}{5000} )}{ln ( 2 )}, n = - \frac{5000 W _{0} ( - \frac{l n ( 2 )}{5000} )}{ln ( 2 )}

+1

十進法表記

n = 81579.60445 \dots, n = 1.00013 \dots

解答ステップ

5000 lo g_{2} (n) = n

以下で両辺を割る

5000

lo g_{2} (n) = \frac{n}{5000}

f (x) = g (x)

ならば,

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

2^{l o g_{2} (n)} = 2^{\frac{n}{5000}}

簡素化

2^{l o g_{2} (n)} : n

n = 2^{\frac{n}{5000}}

解く

n = 2^{\frac{n}{5000}} : n = - \frac{5000 W _{- 1} ( - \frac{l n ( 2 )}{5000} )}{ln ( 2 )}, n = - \frac{5000 W _{0} ( - \frac{l n ( 2 )}{5000} )}{ln ( 2 )}

n = - \frac{5000 W _{- 1} ( - \frac{l n ( 2 )}{5000} )}{ln ( 2 )}, n = - \frac{5000 W _{0} ( - \frac{l n ( 2 )}{5000} )}{ln ( 2 )}

解を検算する:

n = - \frac{5000 W _{- 1} ( - \frac{l n ( 2 )}{5000} )}{ln ( 2 )}

真

, n = - \frac{5000 W _{0} ( - \frac{l n ( 2 )}{5000} )}{ln ( 2 )}

真

解答は

n = - \frac{5000 W _{- 1} ( - \frac{l n ( 2 )}{5000} )}{ln ( 2 )}, n = - \frac{5000 W _{0} ( - \frac{l n ( 2 )}{5000} )}{ln ( 2 )}

グラフ

人気の例

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

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

log_{10}(x)=18.96

lo g_{10} (x) = 18.96

log_{10}(4)-3log_{10}(x+5)=3

lo g_{10} (4) - 3 lo g_{10} (x + 5) = 3

ln (x) = 2.0706

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

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