簡約 (2log_{10}(3)+log_{10}(2))/(log_{10)(3)}

解

簡約

\frac{2 lo g _{10} ( 3 ) + lo g _{10} ( 2 )}{lo g _{10} ( 3 )}

lo g_{3} (18)

十進法表記

2.63092 \dots

解答ステップ

\frac{2 lo g _{10} ( 3 ) + lo g _{10} ( 2 )}{lo g _{10} ( 3 )}

2 lo g_{10} (3) + lo g_{10} (2) = lo g_{10} (18)

= \frac{lo g _{10} ( 18 )}{lo g _{10} ( 3 )}

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} ( 18 )}{lo g _{10} ( 3 )} = lo g_{3} (18)

= lo g_{3} (18)