8225(10295)^n=3750 eching

$$8225 ( 10295 ) ^ { n } = 3750$$

n uchun yechish

$$n=\log_{10295}\left(\frac{150}{329}\right)\approx -0,085007825$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$8225\times 10295^{n}=3750$$

Ikki tarafini 8225 ga bo‘ling.

$$10295^{n}=\frac{150}{329}$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(10295^{n})=\log(\frac{150}{329})$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$n\log(10295)=\log(\frac{150}{329})$$

Ikki tarafini \log(10295) ga bo‘ling.

$$n=\frac{\log(\frac{150}{329})}{\log(10295)}$$

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

$$n=\log_{10295}\left(\frac{150}{329}\right)$$

n uchun yechish (complex solution)

$$n=\frac{2\pi n_{1}i}{\ln(10295)}+\log_{10295}\left(\frac{150}{329}\right)$$

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