103^x=15 eching

$$103 ^ { x } = 15$$

x uchun yechish

$$x=\log_{103}\left(15\right)\approx 0,584295265$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$103^{x}=15$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(103^{x})=\log(15)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$x\log(103)=\log(15)$$

Ikki tarafini \log(103) ga bo‘ling.

$$x=\frac{\log(15)}{\log(103)}$$

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

$$x=\log_{103}\left(15\right)$$

x uchun yechish (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(103)}+\log_{103}\left(15\right)$$

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