簡約 ln(((9x+16y))/((e^{(1))x^{(2)})})

解

簡約

ln (\frac{( 9 x + 16 y )}{( e ^{(1)} x ^{(2)} )})

ln (9 x + 16 y) - 1 - 2 ln (x)

解答ステップ

ln (\frac{( 9 x + 16 y )}{( e ^{(1)} x ^{(2)} )})

対数の規則を適用する:

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

ln (\frac{( 9 x + 16 y )}{( e ^{(1)} x ^{(2)} )}) = ln ((9 x + 16 y)) - ln ((e^{(1)} x^{(2)}))

= ln (9 x + 16 y) - ln (e^{1} x^{2})

対数の規則を適用する:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

ln (e^{1} x^{2}) = ln (e^{1}) + ln (x^{2})

= ln (9 x + 16 y) - (ln (x^{2}) + ln (e^{1}))

対数の規則を適用する:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (e^{1}) = 1 \cdot ln (e)

= ln (9 x + 16 y) - (1 \cdot ln (e) + ln (x^{2}))

対数の規則を適用する:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (x^{2}) = 2 ln (x)

= ln (9 x + 16 y) - (1 \cdot ln (e) + 2 ln (x))

1 \cdot ln (e) = 1

= ln (9 x + 16 y) - (2 ln (x) + 1)

- (1 + 2 ln (x)) : - 1 - 2 ln (x)

= ln (9 x + 16 y) - 1 - 2 ln (x)