(1*1.02)^x=2 eching

$$( 1 \times 1.02 ) ^ { x } = 2$$

x uchun yechish

$$x=\log_{1,02}\left(2\right)\approx 35,002788781$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$1,02^{x}=2$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(1,02^{x})=\log(2)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$x\log(1,02)=\log(2)$$

Ikki tarafini \log(1,02) ga bo‘ling.

$$x=\frac{\log(2)}{\log(1,02)}$$

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

$$x=\log_{1,02}\left(2\right)$$

x uchun yechish (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{\ln(1,02)}+\log_{1,02}\left(2\right)$$

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