9^3x-8=6.561 eching

$$9 ^ { 3 x - 8 } = 6.561$$

x uchun yechish

$$x=-\frac{\log_{3}\left(10\right)}{2}+4\approx 2,952048363$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$9^{3x-8}=6,561$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(9^{3x-8})=\log(6,561)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$\left(3x-8\right)\log(9)=\log(6,561)$$

Ikki tarafini \log(9) ga bo‘ling.

$$3x-8=\frac{\log(6,561)}{\log(9)}$$

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

$$3x-8=\log_{9}\left(6,561\right)$$

8 ni tenglamaning ikkala tarafiga qo'shish.

$$3x=-\frac{3\log_{3}\left(10\right)}{2}+4-\left(-8\right)$$

Ikki tarafini 3 ga bo‘ling.

$$x=\frac{-\frac{3\log_{3}\left(10\right)}{2}+12}{3}$$

x uchun yechish (complex solution)

$$x=\frac{i\pi n_{1}}{3\ln(3)}-\frac{\log_{3}\left(10\right)}{2}+4$$

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