y uchun yechish
y=\ln(11)-9\approx -6,602104727
y uchun yechish (complex solution)
y=\ln(11)-9+2\pi n_{1}i
n_{1}\in \mathrm{Z}
Grafik
Baham ko'rish
Klipbordga nusxa olish
e^{y+9}=11
Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.
\log(e^{y+9})=\log(11)
Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.
\left(y+9\right)\log(e)=\log(11)
Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.
y+9=\frac{\log(11)}{\log(e)}
Ikki tarafini \log(e) ga bo‘ling.
y+9=\log_{e}\left(11\right)
Asosiy tenglamani almashtirish orqali \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).
y=\ln(11)-9
Tenglamaning ikkala tarafidan 9 ni ayirish.
Misollar
Ikkilik tenglama
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometriya
4 \sin \theta \cos \theta = 2 \sin \theta
Chiziqli tenglama
y = 3x + 4
Arifmetik
699 * 533
Matritsa
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simli tenglama
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differensatsiya
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Oʻngga
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Chegaralar
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}