625=1/25*5^n-2 eching

$$625 = \frac { 1 } { 25 } \times 5 ^ { n - 2 }$$

n uchun yechish

$$n=8$$

Logaritm ifodasidan foydalanish qadamlari

Ikki tarafini 25 va teskari kasri \frac{1}{25} ga ko‘paytiring.

$$625\times 25=5^{n-2}$$

15625 hosil qilish uchun 625 va 25 ni ko'paytirish.

$$15625=5^{n-2}$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$5^{n-2}=15625$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(5^{n-2})=\log(15625)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$\left(n-2\right)\log(5)=\log(15625)$$

Ikki tarafini \log(5) ga bo‘ling.

$$n-2=\frac{\log(15625)}{\log(5)}$$

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

$$n-2=\log_{5}\left(15625\right)$$

2 ni tenglamaning ikkala tarafiga qo'shish.

$$n=6-\left(-2\right)$$