11*13^x-14=106 eching

$$11 \times { 13 }^{ x } -14=106$$

x uchun yechish

$$x=\log_{13}\left(\frac{120}{11}\right)\approx 0,931634951$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$11\times 13^{x}-14=106$$

14 ni tenglamaning ikkala tarafiga qo'shish.

$$11\times 13^{x}=120$$

Ikki tarafini 11 ga bo‘ling.

$$13^{x}=\frac{120}{11}$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(13^{x})=\log(\frac{120}{11})$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$x\log(13)=\log(\frac{120}{11})$$

Ikki tarafini \log(13) ga bo‘ling.

$$x=\frac{\log(\frac{120}{11})}{\log(13)}$$

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

$$x=\log_{13}\left(\frac{120}{11}\right)$$

x uchun yechish (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(13)}+\log_{13}\left(\frac{120}{11}\right)$$

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