592*3^2x=74 eching

$$592 \cdot 3 ^ { 2 x } = 74$$

x uchun yechish

$$x=-\frac{3\log_{3}\left(2\right)}{2}\approx -0,94639463$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$592\times 3^{2x}=74$$

Ikki tarafini 592 ga bo‘ling.

$$3^{2x}=\frac{1}{8}$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(3^{2x})=\log(\frac{1}{8})$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$2x\log(3)=\log(\frac{1}{8})$$

Ikki tarafini \log(3) ga bo‘ling.

$$2x=\frac{\log(\frac{1}{8})}{\log(3)}$$

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

$$2x=\log_{3}\left(\frac{1}{8}\right)$$

Ikki tarafini 2 ga bo‘ling.

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

x uchun yechish (complex solution)

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

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