5^x=10 eching

$${ 5 }^{ x } =10$$

x uchun yechish

$$x=\log_{5}\left(10\right)\approx 1,430676558$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$5^{x}=10$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(5^{x})=\log(10)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$x\log(5)=\log(10)$$

Ikki tarafini \log(5) ga bo‘ling.

$$x=\frac{\log(10)}{\log(5)}$$

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

$$x=\log_{5}\left(10\right)$$

x uchun yechish (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(5)}+\log_{5}\left(10\right)$$

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