2^5x=7 eching

$$2 ^ { 5 x } = 7$$

x uchun yechish

$$x=\frac{\log_{2}\left(7\right)}{5}\approx 0,561470984$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$2^{5x}=7$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(2^{5x})=\log(7)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$5x\log(2)=\log(7)$$

Ikki tarafini \log(2) ga bo‘ling.

$$5x=\frac{\log(7)}{\log(2)}$$

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

$$5x=\log_{2}\left(7\right)$$

Ikki tarafini 5 ga bo‘ling.

$$x=\frac{\log_{2}\left(7\right)}{5}$$

x uchun yechish (complex solution)

$$x=\frac{2\pi n_{1}i}{5\ln(2)}+\frac{\log_{2}\left(7\right)}{5}$$

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