7^7/7^3=7^x eching

$$\frac { 7 ^ { 7 } } { 7 ^ { 3 } } = 7 ^ { x }$$

x uchun yechish

$$x=4$$

Logaritm ifodasidan foydalanish qadamlari

Ayni asosning daraja ko‘rsatkichini bo‘lish uchun maxrajning darajasini surat darajasidan ayiring. 7 dan 3 ni ayirib, 4 ni oling.

$$7^{4}=7^{x}$$

4 daraja ko‘rsatkichini 7 ga hisoblang va 2401 ni qiymatni oling.

$$2401=7^{x}$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$7^{x}=2401$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(7^{x})=\log(2401)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$x\log(7)=\log(2401)$$

Ikki tarafini \log(7) ga bo‘ling.

$$x=\frac{\log(2401)}{\log(7)}$$

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

$$x=\log_{7}\left(2401\right)$$

x uchun yechish (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(7)}+4$$

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