frac{5^{m}*5^3*5^-2}{5^-3}=5^1 eching

$$\frac { 5 ^ { m } \times 5 ^ { 3 } \times 5 ^ { - 2 } } { 5 ^ { - 3 } } = 5 ^ { 1 }$$

m uchun yechish

$$m=-3$$

Logaritm ifodasidan foydalanish qadamlari

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 3 va -2 ni qo‘shib, 1 ni oling.

$$\frac{5^{m}\times 5^{1}}{5^{-3}}=5^{1}$$

Ayni asosning daraja ko'rsatkichi bo'lish uchun maxrajning darajasini surat darajasidan bo'ling.

$$5^{4}\times 5^{m}=5^{1}$$

1 daraja ko‘rsatkichini 5 ga hisoblang va 5 ni qiymatni oling.

$$5^{4}\times 5^{m}=5$$

4 daraja ko‘rsatkichini 5 ga hisoblang va 625 ni qiymatni oling.

$$625\times 5^{m}=5$$

Ikki tarafini 625 ga bo‘ling.

$$5^{m}=\frac{5}{625}$$

\frac{5}{625} ulushini 5 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$5^{m}=\frac{1}{125}$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(5^{m})=\log(\frac{1}{125})$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$m\log(5)=\log(\frac{1}{125})$$

Ikki tarafini \log(5) ga bo‘ling.

$$m=\frac{\log(\frac{1}{125})}{\log(5)}$$

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

$$m=\log_{5}\left(\frac{1}{125}\right)$$