化简 ln((2xe^y)^2)+e^{(y+ln(3x))}

解答

化简

ln ((2 x e^{y})^{2}) + e^{(y + l n (3 x))}

2 (ln (2 x) + y) + 3 e^{y} x

求解步骤

ln ((2 x e^{y})^{2}) + e^{y + l n (3 x)}

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

e^{y + l n (3 x)} = 3 e^{y} x

= ln (2^{2} e^{2 y} x^{2}) + 3 e^{y} x

ln (2^{2} x^{2} e^{y \cdot 2}) = 2 (ln (2 x) + y)

= 2 (y + ln (2 x)) + 3 e^{y} x

s im pl i f y \frac{3 x ^{2} + 9 x}{x ^{2} - 9}

s im pl i f y \frac{e ^{- 2} \cdot 2 ^{0}}{0 !}

s im pl i f y 6 (- 5)

s im pl i f y \frac{2 π}{\frac{5}{6}}

s im pl i f y \frac{x ^{2} + 4 x - 12}{x ^{2} ( x ^{2} + 9 x + 18 )} \cdot 6 x^{2}