3*{485}^frac{x{10}}=4000 eching

$$3 \times { 485 }^{ \frac{ x }{ 10 } } = 4000$$

x uchun yechish

$$x=-10\log_{485}\left(\frac{3}{4000}\right)\approx 11,635291256$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$3\times 485^{\frac{1}{10}x}=4000$$

Ikki tarafini 3 ga bo‘ling.

$$485^{\frac{1}{10}x}=\frac{4000}{3}$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(485^{\frac{1}{10}x})=\log(\frac{4000}{3})$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$\frac{1}{10}x\log(485)=\log(\frac{4000}{3})$$

Ikki tarafini \log(485) ga bo‘ling.

$$\frac{1}{10}x=\frac{\log(\frac{4000}{3})}{\log(485)}$$

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

$$\frac{1}{10}x=\log_{485}\left(\frac{4000}{3}\right)$$

Ikkala tarafini 10 ga ko‘paytiring.

$$x=\frac{\ln(\frac{4000}{3})}{\frac{1}{10}\ln(485)}$$

x uchun yechish (complex solution)

$$x=\frac{20\pi n_{1}i}{\ln(485)}-10\log_{485}\left(\frac{3}{4000}\right)$$

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