132^x=8 eching

$${ 132 }^{ x } =8$$

x uchun yechish

$$x=3\log_{132}\left(2\right)\approx 0,42587055$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$132^{x}=8$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(132^{x})=\log(8)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$x\log(132)=\log(8)$$

Ikki tarafini \log(132) ga bo‘ling.

$$x=\frac{\log(8)}{\log(132)}$$

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

$$x=\log_{132}\left(8\right)$$

x uchun yechish (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(132)}+3\log_{132}\left(2\right)$$

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