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人気のある代数 >

5000*log_{10}(n)=n

解

5000 \cdot lo g_{10} (n) = n

解

n = - \frac{5000 W _{- 1} ( - \frac{l n ( 10 )}{5000} )}{ln ( 10 )}, n = - \frac{5000 W _{0} ( - \frac{l n ( 10 )}{5000} )}{ln ( 10 )}

+1

十進法表記

n = 21680.32937 \dots, n = 1.00046 \dots

解答ステップ

5000 lo g_{10} (n) = n

以下で両辺を割る

5000

lo g_{10} (n) = \frac{n}{5000}

f (x) = g (x)

ならば,

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

1 0^{l o g_{10} (n)} = 1 0^{\frac{n}{5000}}

簡素化

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

n = 1 0^{\frac{n}{5000}}

解く

n = 1 0^{\frac{n}{5000}} : n = - \frac{5000 W _{- 1} ( - \frac{l n ( 10 )}{5000} )}{ln ( 10 )}, n = - \frac{5000 W _{0} ( - \frac{l n ( 10 )}{5000} )}{ln ( 10 )}

n = - \frac{5000 W _{- 1} ( - \frac{l n ( 10 )}{5000} )}{ln ( 10 )}, n = - \frac{5000 W _{0} ( - \frac{l n ( 10 )}{5000} )}{ln ( 10 )}

解を検算する:

n = - \frac{5000 W _{- 1} ( - \frac{l n ( 10 )}{5000} )}{ln ( 10 )}

真

, n = - \frac{5000 W _{0} ( - \frac{l n ( 10 )}{5000} )}{ln ( 10 )}

真

解答は

n = - \frac{5000 W _{- 1} ( - \frac{l n ( 10 )}{5000} )}{ln ( 10 )}, n = - \frac{5000 W _{0} ( - \frac{l n ( 10 )}{5000} )}{ln ( 10 )}

グラフ

人気の例

6.5=-log_{10}(x)

6.5 = - lo g_{10} (x)

2log_{2}(y)+log_{4}(y)=9

2 lo g_{2} (y) + lo g_{4} (y) = 9

x-1=log_{2}(3^x)

x - 1 = lo g_{2} (3^{x})

solvefor y,log_{5}(y)=x

so l v e f or y, lo g_{5} (y) = x

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

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