12(25)^x-1=75 eching

$$12 ( 25 ) ^ { x - 1 } = 75$$

x uchun yechish

$$x=-\log_{5}\left(2\right)+2\approx 1,569323442$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$12\times 25^{x-1}=75$$

Ikki tarafini 12 ga bo‘ling.

$$25^{x-1}=\frac{25}{4}$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(25^{x-1})=\log(\frac{25}{4})$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$\left(x-1\right)\log(25)=\log(\frac{25}{4})$$

Ikki tarafini \log(25) ga bo‘ling.

$$x-1=\frac{\log(\frac{25}{4})}{\log(25)}$$

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

$$x-1=\log_{25}\left(\frac{25}{4}\right)$$

1 ni tenglamaning ikkala tarafiga qo'shish.

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

x uchun yechish (complex solution)

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

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