1/4=5^x eching

$$\frac{ 1 }{ 4 } = { 5 }^{ x }$$

x uchun yechish

$$x=-2\log_{5}\left(2\right)\approx -0,861353116$$

Logaritm ifodasidan foydalanish qadamlari

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$5^{x}=\frac{1}{4}$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(5^{x})=\log(\frac{1}{4})$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$x\log(5)=\log(\frac{1}{4})$$

Ikki tarafini \log(5) ga bo‘ling.

$$x=\frac{\log(\frac{1}{4})}{\log(5)}$$

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

$$x=\log_{5}\left(\frac{1}{4}\right)$$

x uchun yechish (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(5)}-2\log_{5}\left(2\right)$$

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