3^5x-2=4 eching

$$3 ^ { 5 x - 2 } = 4$$

x uchun yechish

$$x=\frac{2\left(\log_{3}\left(2\right)+1\right)}{5}\approx 0,652371901$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$3^{5x-2}=4$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(3^{5x-2})=\log(4)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$\left(5x-2\right)\log(3)=\log(4)$$

Ikki tarafini \log(3) ga bo‘ling.

$$5x-2=\frac{\log(4)}{\log(3)}$$

Asosiy tenglamani almashtirish orqali \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).

$$5x-2=\log_{3}\left(4\right)$$

2 ni tenglamaning ikkala tarafiga qo'shish.

$$5x=2\log_{3}\left(2\right)-\left(-2\right)$$

Ikki tarafini 5 ga bo‘ling.

$$x=\frac{2\log_{3}\left(2\right)+2}{5}$$

x uchun yechish (complex solution)

$$x=\frac{2\pi n_{1}i}{5\ln(3)}+\frac{2\log_{3}\left(6\right)}{5}$$

$$n_{1}\in \mathrm{Z}$$