3^x+118/3=19 eching

$${ 3 }^{ x+1 } \frac{ 18 }{ 3 } =19$$

x uchun yechish

$$x=-\log_{3}\left(\frac{2}{19}\right)-2\approx 0,049214106$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$6\times 3^{x+1}=19$$

Ikki tarafini 6 ga bo‘ling.

$$3^{x+1}=\frac{19}{6}$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(3^{x+1})=\log(\frac{19}{6})$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$\left(x+1\right)\log(3)=\log(\frac{19}{6})$$

Ikki tarafini \log(3) ga bo‘ling.

$$x+1=\frac{\log(\frac{19}{6})}{\log(3)}$$

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

$$x+1=\log_{3}\left(\frac{19}{6}\right)$$

Tenglamaning ikkala tarafidan 1 ni ayirish.

$$x=\frac{\ln(\frac{19}{6})}{\ln(3)}-1$$

x uchun yechish (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(3)}-\log_{3}\left(\frac{2}{19}\right)-2$$

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