4^3x=512 eching

$$4 ^ { 3 x } = 512$$

x uchun yechish

$$x = \frac{3}{2} = 1\frac{1}{2} = 1,5$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$4^{3x}=512$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(4^{3x})=\log(512)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$3x\log(4)=\log(512)$$

Ikki tarafini \log(4) ga bo‘ling.

$$3x=\frac{\log(512)}{\log(4)}$$

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

$$3x=\log_{4}\left(512\right)$$

Ikki tarafini 3 ga bo‘ling.

$$x=\frac{\frac{9}{2}}{3}$$

x uchun yechish (complex solution)

$$x=\frac{i\pi n_{1}}{3\ln(2)}+\frac{3}{2}$$

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