簡約 ln(49)*log_{7}(e^2)

解

簡約

ln (49) \cdot lo g_{7} (e^{2})

4

解答ステップ

ln (49) lo g_{7} (e^{2})

簡素化

lo g_{7} (e^{2}) : 2 lo g_{7} (e)

= 2 ln (49) lo g_{7} (e)

対数の規則を適用する:

lo g_{a} (b) = \frac{ln ( b )}{ln ( a )}

ln (49) lo g_{7} (e) = \frac{ln ( 49 )}{ln ( e )} \cdot \frac{ln ( e )}{ln ( 7 )}

= 2 \cdot \frac{ln ( 49 )}{ln ( e )} \cdot \frac{ln ( e )}{ln ( 7 )}

改良

= 2 \cdot \frac{ln ( 49 )}{ln ( 7 )}

分数を乗じる:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{ln ( 49 ) \cdot 2}{ln ( 7 )}

簡素化

ln (49) : 2 ln (7)

= \frac{2 \cdot 2 ln ( 7 )}{ln ( 7 )}

数を乗じる:

2 \cdot 2 = 4

= \frac{4 ln ( 7 )}{ln ( 7 )}

共通因数を約分する:

ln (7)

= 4