(100)(102^2x)=500000 eching

$$(100)( { 102 }^{ 2x } )=500000$$

x uchun yechish

$$x=\frac{\log_{102}\left(5000\right)}{2}\approx 0,920783055$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$100\times 102^{2x}=500000$$

Ikki tarafini 100 ga bo‘ling.

$$102^{2x}=5000$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(102^{2x})=\log(5000)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$2x\log(102)=\log(5000)$$

Ikki tarafini \log(102) ga bo‘ling.

$$2x=\frac{\log(5000)}{\log(102)}$$

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

$$2x=\log_{102}\left(5000\right)$$

Ikki tarafini 2 ga bo‘ling.

$$x=\frac{\log_{102}\left(5000\right)}{2}$$

x uchun yechish (complex solution)

$$x=\frac{\pi n_{1}i}{\ln(102)}+\frac{\log_{102}\left(5000\right)}{2}$$

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