3^x+2=3^5 eching

$$3 ^ { x + 2 } = 3 ^ { 5 }$$

x uchun yechish

$$x=3$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$3^{x+2}=243$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(3^{x+2})=\log(243)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$\left(x+2\right)\log(3)=\log(243)$$

Ikki tarafini \log(3) ga bo‘ling.

$$x+2=\frac{\log(243)}{\log(3)}$$

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

$$x+2=\log_{3}\left(243\right)$$

Tenglamaning ikkala tarafidan 2 ni ayirish.

$$x=5-2$$

x uchun yechish (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{\ln(3)}+3$$

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