化简 ln(x)+1/2*ln(1+(y^2)/(x^2))

解答

化简

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

ln (x^{2} + y^{2})

求解步骤

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

使用对数计算法则:

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

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

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

使用对数计算法则:

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

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

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

化简

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

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

s im pl i f y lo g_{5} (3) + 4 lo g_{5} (y)

j o in \frac{2}{3} lo g_{10} (2)

s im pl i f y 6 ln (\frac{36.5}{6})

s im pl i f y - 25 lo g_{10} (3) + 25 lo g_{10} (7)

s im pl i f y ln (4.4 \cdot 1 0^{9})