3^x+1=(27*3)^4 eching

$$3 ^ { x + 1 } = ( 27 \cdot 3 ) ^ { 4 }$$

x uchun yechish

$$x=15$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$3^{x+1}=43046721$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(3^{x+1})=\log(43046721)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$\left(x+1\right)\log(3)=\log(43046721)$$

Ikki tarafini \log(3) ga bo‘ling.

$$x+1=\frac{\log(43046721)}{\log(3)}$$

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

$$x+1=\log_{3}\left(43046721\right)$$

Tenglamaning ikkala tarafidan 1 ni ayirish.

$$x=16-1$$

x uchun yechish (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{\ln(3)}+15$$

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