10(107)^x=2000 eching

$$10 ( 107 ) ^ { x } = 2000$$

x uchun yechish

$$x=\log_{107}\left(200\right)\approx 1,133856504$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$10\times 107^{x}=2000$$

Ikki tarafini 10 ga bo‘ling.

$$107^{x}=200$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(107^{x})=\log(200)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$x\log(107)=\log(200)$$

Ikki tarafini \log(107) ga bo‘ling.

$$x=\frac{\log(200)}{\log(107)}$$

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

$$x=\log_{107}\left(200\right)$$

x uchun yechish (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(107)}+\log_{107}\left(200\right)$$

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