546978=4500*105^n eching

$$546978 = 4500 \times 105 ^ { n }$$

n uchun yechish

$$n=\log_{105}\left(\frac{91163}{750}\right)\approx 1,031450813$$

Logaritm ifodasidan foydalanish qadamlari

Ikki tarafini 4500 ga bo‘ling.

$$\frac{546978}{4500}=105^{n}$$

\frac{546978}{4500} ulushini 6 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{91163}{750}=105^{n}$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$105^{n}=\frac{91163}{750}$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(105^{n})=\log(\frac{91163}{750})$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$n\log(105)=\log(\frac{91163}{750})$$

Ikki tarafini \log(105) ga bo‘ling.

$$n=\frac{\log(\frac{91163}{750})}{\log(105)}$$

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

$$n=\log_{105}\left(\frac{91163}{750}\right)$$