(1*102)^x=2 eching

$$( 1 \times 102 ) ^ { x } = 2$$

x uchun yechish

$$x=\log_{102}\left(2\right)\approx 0,149870542$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$102^{x}=2$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(102^{x})=\log(2)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$x\log(102)=\log(2)$$

Ikki tarafini \log(102) ga bo‘ling.

$$x=\frac{\log(2)}{\log(102)}$$

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

$$x=\log_{102}\left(2\right)$$

x uchun yechish (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(102)}+\log_{102}\left(2\right)$$

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