749^x+2=49 eching

$$749 ^ { x + 2 } = 49$$

x uchun yechish

$$x=-2\log_{749}\left(107\right)\approx -1,411999732$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$749^{x+2}=49$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(749^{x+2})=\log(49)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$\left(x+2\right)\log(749)=\log(49)$$

Ikki tarafini \log(749) ga bo‘ling.

$$x+2=\frac{\log(49)}{\log(749)}$$

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

$$x+2=\log_{749}\left(49\right)$$

Tenglamaning ikkala tarafidan 2 ni ayirish.

$$x=2\log_{749}\left(7\right)-2$$

x uchun yechish (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(749)}-2\log_{749}\left(107\right)$$

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