102*(102^x-1)=11*002 eching

$$102 \times ( { 102 }^{ x } -1)=11 \times 002$$

x uchun yechish

$$x=0$$

Logaritm ifodasidan foydalanish qadamlari

102 ga 102^{x}-1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$102\times 102^{x}-102=11\times 0\times 0\times 2$$

0 hosil qilish uchun 11 va 0 ni ko'paytirish.

$$102\times 102^{x}-102=0\times 0\times 2$$

0 hosil qilish uchun 0 va 0 ni ko'paytirish.

$$102\times 102^{x}-102=0\times 2$$

0 hosil qilish uchun 0 va 2 ni ko'paytirish.

$$102\times 102^{x}-102=0$$

102 ni tenglamaning ikkala tarafiga qo'shish.

$$102\times 102^{x}=102$$

Ikki tarafini 102 ga bo‘ling.

$$102^{x}=1$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(102^{x})=\log(1)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$x\log(102)=\log(1)$$

Ikki tarafini \log(102) ga bo‘ling.

$$x=\frac{\log(1)}{\log(102)}$$

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

$$x=\log_{102}\left(1\right)$$

x uchun yechish (complex solution)

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

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