e^-9x=72 eching

$$e ^ { - 9 x } = 72$$

x uchun yechish

$$x=-\frac{\ln(72)}{9}\approx -0,475185124$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$e^{-9x}=72$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(e^{-9x})=\log(72)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$-9x\log(e)=\log(72)$$

Ikki tarafini \log(e) ga bo‘ling.

$$-9x=\frac{\log(72)}{\log(e)}$$

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

$$-9x=\log_{e}\left(72\right)$$

Ikki tarafini -9 ga bo‘ling.

$$x=\frac{\ln(72)}{-9}$$

x uchun yechish (complex solution)

$$x=-\frac{i\times 2\pi n_{1}}{9}-\frac{\ln(72)}{9}$$

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