簡約 1/2*ln(t^2(x^2+y^2))

解

簡約

\frac{1}{2} \cdot ln (t^{2} (x^{2} + y^{2}))

ln (t) + \frac{1}{2} ln (x^{2} + y^{2})

解答ステップ

\frac{1}{2} ln (t^{2} (x^{2} + y^{2}))

対数の規則を適用する:

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

\frac{1}{2} ln (t^{2} (x^{2} + y^{2})) = \frac{1}{2} ln (t^{2}) + \frac{1}{2} ln (x^{2} + y^{2})

= \frac{1}{2} ln (t^{2}) + \frac{1}{2} ln (x^{2} + y^{2})

対数の規則を適用する:

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

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

= \frac{1}{2} \cdot 2 ln (t) + \frac{1}{2} ln (x^{2} + y^{2})

\frac{1}{2} \cdot 2 ln (t) = ln (t)

= ln (t) + \frac{1}{2} ln (x^{2} + y^{2})