x uchun yechish
x=3
x uchun yechish (complex solution)
x=\frac{i\times 2\pi n_{1}}{3\ln(5)}+3
n_{1}\in \mathrm{Z}
Grafik
Baham ko'rish
Klipbordga nusxa olish
5^{3x-7}=25
Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.
\log(5^{3x-7})=\log(25)
Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.
\left(3x-7\right)\log(5)=\log(25)
Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.
3x-7=\frac{\log(25)}{\log(5)}
Ikki tarafini \log(5) ga bo‘ling.
3x-7=\log_{5}\left(25\right)
Asosiy tenglamani almashtirish orqali \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).
3x=2-\left(-7\right)
7 ni tenglamaning ikkala tarafiga qo'shish.
x=\frac{9}{3}
Ikki tarafini 3 ga bo‘ling.
Misollar
Ikkilik tenglama
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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}