3*4^x=9 eching

$$3 \cdot 4 ^ { x } = 9$$

x uchun yechish

$$x=\frac{\log_{2}\left(3\right)}{2}\approx 0,79248125$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$3\times 4^{x}=9$$

Ikki tarafini 3 ga bo‘ling.

$$4^{x}=3$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

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

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

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

Ikki tarafini \log(4) ga bo‘ling.

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

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

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

x uchun yechish (complex solution)

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

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