3e^2-3n+3=54 eching

$$3 e ^ { 2 - 3 n } + 3 = 54$$

n uchun yechish

$$n=\frac{2-\ln(17)}{3}\approx -0,277737781$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$3e^{-3n+2}+3=54$$

Tenglamaning ikkala tarafidan 3 ni ayirish.

$$3e^{-3n+2}=51$$

Ikki tarafini 3 ga bo‘ling.

$$e^{-3n+2}=17$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(e^{-3n+2})=\log(17)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$\left(-3n+2\right)\log(e)=\log(17)$$

Ikki tarafini \log(e) ga bo‘ling.

$$-3n+2=\frac{\log(17)}{\log(e)}$$

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

$$-3n+2=\log_{e}\left(17\right)$$

Tenglamaning ikkala tarafidan 2 ni ayirish.

$$-3n=\ln(17)-2$$

Ikki tarafini -3 ga bo‘ling.

$$n=\frac{\ln(17)-2}{-3}$$