3^23*3^x*3^19=3^78 eching

$$3 ^ { 23 } \times 3 ^ { x } \times 3 ^ { 19 } = 3 ^ { 78 }$$

x uchun yechish

$$x=36$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$109418989131512359209\times 3^{x}=16423203268260658146231467800709255289$$

Ikki tarafini 109418989131512359209 ga bo‘ling.

$$3^{x}=150094635296999121$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(3^{x})=\log(150094635296999121)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$x\log(3)=\log(150094635296999121)$$

Ikki tarafini \log(3) ga bo‘ling.

$$x=\frac{\log(150094635296999121)}{\log(3)}$$

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

$$x=\log_{3}\left(150094635296999121\right)$$

x uchun yechish (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(3)}+36$$

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