簡約 ln(4x)+3ln(x/2)+ln(2x^2)

解

簡約

ln (4 x) + 3 ln (\frac{x}{2}) + ln (2 x^{2})

ln (x^{6})

解答ステップ

ln (4 x) + 3 ln (\frac{x}{2}) + ln (2 x^{2})

対数の規則を適用する:

a lo g_{c} (b) = lo g_{c} (b^{a})

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

= ln (4 x) + ln ((\frac{x}{2})^{3}) + ln (2 x^{2})

対数の規則を適用する:

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

ln (4 x) + ln ((\frac{x}{2})^{3}) = ln (4 (\frac{x}{2})^{3} x)

= ln (4 (\frac{x}{2})^{3} x) + ln (2 x^{2})

簡素化

4 x (\frac{x}{2})^{3} : \frac{x ^{4}}{2}

= ln (\frac{x ^{4}}{2}) + ln (2 x^{2})

対数の規則を適用する:

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

ln (\frac{x ^{4}}{2}) + ln (2 x^{2}) = ln (2 \cdot \frac{x ^{4}}{2} x^{2})

= ln (2 \cdot \frac{x ^{4}}{2} x^{2})

簡素化

\frac{x ^{4}}{2} \cdot 2 x^{2} : x^{6}

= ln (x^{6})