(118)^x-1/18=20 eching

$$\frac { ( 118 ) ^ { x } - 1 } { 18 } = 20$$

x uchun yechish

$$x=2\log_{118}\left(19\right)\approx 1,234388441$$

Logaritm ifodasidan foydalanish qadamlari

Ikkala tarafini 18 ga ko‘paytiring.

$$118^{x}-1=20\times 18$$

360 hosil qilish uchun 20 va 18 ni ko'paytirish.

$$118^{x}-1=360$$

1 ni tenglamaning ikkala tarafiga qo'shish.

$$118^{x}=361$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(118^{x})=\log(361)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$x\log(118)=\log(361)$$

Ikki tarafini \log(118) ga bo‘ling.

$$x=\frac{\log(361)}{\log(118)}$$

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

$$x=\log_{118}\left(361\right)$$

x uchun yechish (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(118)}+2\log_{118}\left(19\right)$$

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