5^-x=4 eching

$$5 ^ { - x } = 4$$

x uchun yechish

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

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$5^{-x}=4$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

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

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$-x\log(5)=\log(4)$$

Ikki tarafini \log(5) ga bo‘ling.

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

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

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

Ikki tarafini -1 ga bo‘ling.

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

x uchun yechish (complex solution)

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

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