簡約-log_{10}(2.29x)10^{-7}

解

簡約

- lo g_{10} (2.29 x) 1 0^{- 7}

\frac{1}{5000000} - \frac{lo g _{10} ( 229 ) + lo g _{10} ( x )}{10000000}

解答ステップ

- lo g_{10} (2.29 x) \cdot 1 0^{- 7}

簡素化

lo g_{10} (2.29 x) : lo g_{10} (229 x) - 2

= - (lo g_{10} (229 x) - 2) \cdot 1 0^{- 7}

簡素化

- (lo g_{10} (229 x) - 2) \cdot 1 0^{- 7} : - \frac{1}{10000000} lo g_{10} (229) - \frac{lo g _{10} ( x )}{10000000} + \frac{1}{5000000}

= - \frac{1}{10000000} lo g_{10} (229) - \frac{lo g _{10} ( x )}{10000000} + \frac{1}{5000000}

乗じる

\frac{1}{10000000} lo g_{10} (229) : \frac{lo g _{10} ( 229 )}{10000000}

= - \frac{lo g _{10} ( 229 )}{10000000} - \frac{lo g _{10} ( x )}{10000000} + \frac{1}{5000000}

分数を組み合わせる

- \frac{lo g _{10} ( 229 )}{10000000} - \frac{lo g _{10} ( x )}{10000000} : - \frac{lo g _{10} ( 229 x )}{10000000}

= \frac{1}{5000000} - \frac{lo g _{10} ( 229 x )}{10000000}

対数の規則を適用する:

lo g_{a} (x y) = lo g_{a} (x) + lo g_{a} (y)

lo g_{10} (229 x) = lo g_{10} (229) + lo g_{10} (x)

= \frac{1}{5000000} - \frac{lo g _{10} ( 229 ) + lo g _{10} ( x )}{10000000}