10095^x=4 eching

$${ 10095 }^{ x } =4$$

x uchun yechish

$$x=2\log_{10095}\left(2\right)\approx 0,15036064$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$10095^{x}=4$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(10095^{x})=\log(4)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$x\log(10095)=\log(4)$$

Ikki tarafini \log(10095) ga bo‘ling.

$$x=\frac{\log(4)}{\log(10095)}$$

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

$$x=\log_{10095}\left(4\right)$$

x uchun yechish (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(10095)}+2\log_{10095}\left(2\right)$$

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