180434=10225^4x eching

$$180434= { 10225 }^{ 4x }$$

x uchun yechish

$$x=\frac{\log_{10225}\left(180434\right)}{4}\approx 0,327728163$$

Logaritm ifodasidan foydalanish qadamlari

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$10225^{4x}=180434$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(10225^{4x})=\log(180434)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$4x\log(10225)=\log(180434)$$

Ikki tarafini \log(10225) ga bo‘ling.

$$4x=\frac{\log(180434)}{\log(10225)}$$

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

$$4x=\log_{10225}\left(180434\right)$$

Ikki tarafini 4 ga bo‘ling.

$$x=\frac{\log_{10225}\left(180434\right)}{4}$$

x uchun yechish (complex solution)

$$x=\frac{\pi n_{1}i}{2\ln(10225)}+\frac{\log_{10225}\left(180434\right)}{4}$$

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