12^x+3=15 eching

$${ 12 }^{ x+3 } =15$$

x uchun yechish

$$x=-\log_{12}\left(\frac{576}{5}\right)\approx -1,910200429$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$12^{x+3}=15$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(12^{x+3})=\log(15)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$\left(x+3\right)\log(12)=\log(15)$$

Ikki tarafini \log(12) ga bo‘ling.

$$x+3=\frac{\log(15)}{\log(12)}$$

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

$$x+3=\log_{12}\left(15\right)$$

Tenglamaning ikkala tarafidan 3 ni ayirish.

$$x=\log_{12}\left(15\right)-3$$

x uchun yechish (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(12)}-\log_{12}\left(\frac{576}{5}\right)$$

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