2^-5x=9 eching

$$2 ^ { - 5 x } = 9$$

x uchun yechish

$$x=-\frac{2\log_{2}\left(3\right)}{5}\approx -0,633985$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$2^{-5x}=9$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(2^{-5x})=\log(9)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$-5x\log(2)=\log(9)$$

Ikki tarafini \log(2) ga bo‘ling.

$$-5x=\frac{\log(9)}{\log(2)}$$

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

$$-5x=\log_{2}\left(9\right)$$

Ikki tarafini -5 ga bo‘ling.

$$x=\frac{2\log_{2}\left(3\right)}{-5}$$

x uchun yechish (complex solution)

$$x=-\frac{2\pi n_{1}i}{5\ln(2)}-\frac{2\log_{2}\left(3\right)}{5}$$

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