3000*1032^x=6000 eching

$$3000 \times { 1032 }^{ x } =6000$$

x uchun yechish

$$x=\log_{1032}\left(2\right)\approx 0,099887853$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$3000\times 1032^{x}=6000$$

Ikki tarafini 3000 ga bo‘ling.

$$1032^{x}=2$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(1032^{x})=\log(2)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$x\log(1032)=\log(2)$$

Ikki tarafini \log(1032) ga bo‘ling.

$$x=\frac{\log(2)}{\log(1032)}$$

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

$$x=\log_{1032}\left(2\right)$$

x uchun yechish (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(1032)}+\log_{1032}\left(2\right)$$

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