0.99+left(1-0.25right)^N=1 eching

$$0.99+{\left(1-0.25\right)}^{N}=1$$

N uchun yechish

$$N=-2\log_{0,75}\left(10\right)\approx 16,007845559$$

Logaritm ifodasidan foydalanish qadamlari

0,75 olish uchun 1 dan 0,25 ni ayirish.

$$0,99+0,75^{N}=1$$

Ikkala tarafdan 1 ni ayirish.

$$0,99+0,75^{N}-1=0$$

-0,01 olish uchun 0,99 dan 1 ni ayirish.

$$-0,01+0,75^{N}=0$$

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$0,75^{N}-0,01=0$$

0,01 ni tenglamaning ikkala tarafiga qo'shish.

$$0,75^{N}=0,01$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(0,75^{N})=\log(0,01)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$N\log(0,75)=\log(0,01)$$

Ikki tarafini \log(0,75) ga bo‘ling.

$$N=\frac{\log(0,01)}{\log(0,75)}$$

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

$$N=\log_{0,75}\left(0,01\right)$$