400000=200000*104^x eching

$$400000=200000 \times { 104 }^{ x }$$

x uchun yechish

$$x=\log_{104}\left(2\right)\approx 0,149243937$$

Logaritm ifodasidan foydalanish qadamlari

Ikki tarafini 200000 ga bo‘ling.

$$\frac{400000}{200000}=104^{x}$$

2 ni olish uchun 400000 ni 200000 ga bo‘ling.

$$2=104^{x}$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$104^{x}=2$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(104^{x})=\log(2)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$x\log(104)=\log(2)$$

Ikki tarafini \log(104) ga bo‘ling.

$$x=\frac{\log(2)}{\log(104)}$$

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

$$x=\log_{104}\left(2\right)$$

x uchun yechish (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(104)}+\log_{104}\left(2\right)$$

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