10^1-x=5 eching

$$10 ^ { 1 - x } = 5$$

x uchun yechish

$$x=\log_{10}\left(2\right)\approx 0,301029996$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$10^{-x+1}=5$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(10^{-x+1})=\log(5)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$\left(-x+1\right)\log(10)=\log(5)$$

Tenglamaning ikkala tarafidan 1 ni ayirish.

$$-x=\log(5)-1$$

Ikki tarafini -1 ga bo‘ling.

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

x uchun yechish (complex solution)

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

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