7^x-3=6 eching

$$7 ^ { x - 3 } = 6$$

x uchun yechish

$$x=\log_{7}\left(6\right)+3\approx 3,920782221$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$7^{x-3}=6$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(7^{x-3})=\log(6)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$\left(x-3\right)\log(7)=\log(6)$$

Ikki tarafini \log(7) ga bo‘ling.

$$x-3=\frac{\log(6)}{\log(7)}$$

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

$$x-3=\log_{7}\left(6\right)$$

3 ni tenglamaning ikkala tarafiga qo'shish.

$$x=\log_{7}\left(6\right)-\left(-3\right)$$

x uchun yechish (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{\ln(7)}+\log_{7}\left(6\right)+3$$

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