6^-3x=4 eching

$$6 ^ { - 3 x } = 4$$

x uchun yechish

$$x=-\frac{2\log_{6}\left(2\right)}{3}\approx -0,257901871$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$6^{-3x}=4$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(6^{-3x})=\log(4)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$-3x\log(6)=\log(4)$$

Ikki tarafini \log(6) ga bo‘ling.

$$-3x=\frac{\log(4)}{\log(6)}$$

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

$$-3x=\log_{6}\left(4\right)$$

Ikki tarafini -3 ga bo‘ling.

$$x=\frac{2\log_{6}\left(2\right)}{-3}$$

x uchun yechish (complex solution)

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

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