4^6x-2=45 eching

$$4 ^ { 6 x - 2 } = 45$$

x uchun yechish

$$x=\frac{\log_{2}\left(45\right)}{12}+\frac{1}{3}\approx 0,790987758$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$4^{6x-2}=45$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(4^{6x-2})=\log(45)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$\left(6x-2\right)\log(4)=\log(45)$$

Ikki tarafini \log(4) ga bo‘ling.

$$6x-2=\frac{\log(45)}{\log(4)}$$

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

$$6x-2=\log_{4}\left(45\right)$$

2 ni tenglamaning ikkala tarafiga qo'shish.

$$6x=\frac{\log_{2}\left(45\right)}{2}-\left(-2\right)$$

Ikki tarafini 6 ga bo‘ling.

$$x=\frac{\frac{\log_{2}\left(45\right)}{2}+2}{6}$$

x uchun yechish (complex solution)

$$x=\frac{\pi n_{1}i}{6\ln(2)}+\frac{\log_{2}\left(45\right)}{12}+\frac{1}{3}$$

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