3^alpha-5*3+6=0 eching

$$3 ^ { \alpha } - 5 \times 3 + 6 = 0$$

α uchun yechish

$$\alpha =2$$

Logaritm ifodasidan foydalanish qadamlari

Shartlarni qayta saralash.

$$-5\times 3+3^{\alpha }+6=0$$

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$3^{\alpha }-9=0$$

9 ni tenglamaning ikkala tarafiga qo'shish.

$$3^{\alpha }=9$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(3^{\alpha })=\log(9)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$\alpha \log(3)=\log(9)$$

Ikki tarafini \log(3) ga bo‘ling.

$$\alpha =\frac{\log(9)}{\log(3)}$$

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

$$\alpha =\log_{3}\left(9\right)$$