6200=990(1115)^x+2900 eching

$$6200 = 990 ( 1115 ) ^ { x } + 2900$$

x uchun yechish

$$x=\log_{1115}\left(\frac{10}{3}\right)\approx 0,171588967$$

Logaritm ifodasidan foydalanish qadamlari

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$990\times 1115^{x}+2900=6200$$

Tenglamaning ikkala tarafidan 2900 ni ayirish.

$$990\times 1115^{x}=3300$$

Ikki tarafini 990 ga bo‘ling.

$$1115^{x}=\frac{10}{3}$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(1115^{x})=\log(\frac{10}{3})$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$x\log(1115)=\log(\frac{10}{3})$$

Ikki tarafini \log(1115) ga bo‘ling.

$$x=\frac{\log(\frac{10}{3})}{\log(1115)}$$

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

$$x=\log_{1115}\left(\frac{10}{3}\right)$$

x uchun yechish (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(1115)}+\log_{1115}\left(\frac{10}{3}\right)$$

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