6*e^y=200 eching

$$6 \cdot e ^ { y } = 200$$

y uchun yechish

$$y=-\ln(\frac{3}{100})\approx 3,506557897$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$6e^{y}=200$$

Ikki tarafini 6 ga bo‘ling.

$$e^{y}=\frac{100}{3}$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(e^{y})=\log(\frac{100}{3})$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$y\log(e)=\log(\frac{100}{3})$$

Ikki tarafini \log(e) ga bo‘ling.

$$y=\frac{\log(\frac{100}{3})}{\log(e)}$$

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

$$y=\log_{e}\left(\frac{100}{3}\right)$$

y uchun yechish (complex solution)

$$y=-\ln(\frac{3}{100})+2\pi n_{1}i$$

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