1324=870*10375^n eching

$$1324 = 870 \cdot 10375 ^ { n }$$

n uchun yechish

$$n=\log_{10375}\left(\frac{662}{435}\right)\approx 0,045410675$$

Logaritm ifodasidan foydalanish qadamlari

Ikki tarafini 870 ga bo‘ling.

$$\frac{1324}{870}=10375^{n}$$

\frac{1324}{870} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{662}{435}=10375^{n}$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$10375^{n}=\frac{662}{435}$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(10375^{n})=\log(\frac{662}{435})$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$n\log(10375)=\log(\frac{662}{435})$$

Ikki tarafini \log(10375) ga bo‘ling.

$$n=\frac{\log(\frac{662}{435})}{\log(10375)}$$

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

$$n=\log_{10375}\left(\frac{662}{435}\right)$$