簡約 log_{2}(6)*log_{6}(8)

解

簡約

lo g_{2} (6) \cdot lo g_{6} (8)

3

解答ステップ

lo g_{2} (6) lo g_{6} (8)

対数の規則を適用する:

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

lo g_{2} (6) = \frac{ln ( 6 )}{ln ( 2 )}

= \frac{ln ( 6 )}{ln ( 2 )} lo g_{6} (8)

対数の規則を適用する:

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

lo g_{6} (8) = \frac{ln ( 8 )}{ln ( 6 )}

= \frac{ln ( 6 )}{ln ( 2 )} \cdot \frac{ln ( 8 )}{ln ( 6 )}

共通因数をクロス約分する:

ln (6)

= \frac{ln ( 8 )}{ln ( 2 )}

ln (8) = 3 ln (2)

= \frac{3 ln ( 2 )}{ln ( 2 )}

共通因数を約分する:

ln (2)

= 3