e^a-1=1/2 eching

$$e ^ { a - 1 } = \frac { 1 } { 2 }$$

a uchun yechish

$$a=1-\ln(2)\approx 0,306852819$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$e^{a-1}=\frac{1}{2}$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(e^{a-1})=\log(\frac{1}{2})$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$\left(a-1\right)\log(e)=\log(\frac{1}{2})$$

Ikki tarafini \log(e) ga bo‘ling.

$$a-1=\frac{\log(\frac{1}{2})}{\log(e)}$$

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

$$a-1=\log_{e}\left(\frac{1}{2}\right)$$

1 ni tenglamaning ikkala tarafiga qo'shish.

$$a=-\ln(2)-\left(-1\right)$$