700*(102)^x=800 eching

$$700 \times ( 102 ) ^ { x } = 800$$

x uchun yechish

$$x=\log_{102}\left(\frac{8}{7}\right)\approx 0,028871822$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$700\times 102^{x}=800$$

Ikki tarafini 700 ga bo‘ling.

$$102^{x}=\frac{8}{7}$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(102^{x})=\log(\frac{8}{7})$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$x\log(102)=\log(\frac{8}{7})$$

Ikki tarafini \log(102) ga bo‘ling.

$$x=\frac{\log(\frac{8}{7})}{\log(102)}$$

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

$$x=\log_{102}\left(\frac{8}{7}\right)$$

x uchun yechish (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(102)}+\log_{102}\left(\frac{8}{7}\right)$$

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