7^x+2=4 eching

$$7 ^ { x } + 2 = 4$$

x uchun yechish

$$x=\log_{7}\left(2\right)\approx 0,356207187$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$7^{x}+2=4$$

Tenglamaning ikkala tarafidan 2 ni ayirish.

$$7^{x}=2$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(7^{x})=\log(2)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$x\log(7)=\log(2)$$

Ikki tarafini \log(7) ga bo‘ling.

$$x=\frac{\log(2)}{\log(7)}$$

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

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

x uchun yechish (complex solution)

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

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