簡約 (log_{10}(2))/(log_{10)(5)-log_{10}(2)}

解

簡約

\frac{lo g _{10} ( 2 )}{lo g _{10} ( 5 ) - lo g _{10} ( 2 )}

lo g_{\frac{5}{2}} (2)

十進法表記

0.75647 \dots

解答ステップ

\frac{lo g _{10} ( 2 )}{lo g _{10} ( 5 ) - lo g _{10} ( 2 )}

対数の規則を適用する:

lo g_{a} (x) - lo g_{a} (y) = lo g_{a} (\frac{x}{y})

lo g_{10} (5) - lo g_{10} (2) = lo g_{10} (\frac{5}{2})

= \frac{lo g _{10} ( 2 )}{lo g _{10} ( \frac{5}{2} )}

対数の規則を適用する:

\frac{lo g _{c} ( b )}{lo g _{c} ( a )} = lo g_{a} (b)

\frac{lo g _{10} ( 2 )}{lo g _{10} ( \frac{5}{2} )} = lo g_{\frac{5}{2}} (2)

= lo g_{\frac{5}{2}} (2)