6^22x-3=1 eching

$${ 6 }^{ 22x-3 } =1$$

x uchun yechish

$$x=\frac{3}{22}\approx 0,136363636$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$6^{22x-3}=1$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(6^{22x-3})=\log(1)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$\left(22x-3\right)\log(6)=\log(1)$$

Ikki tarafini \log(6) ga bo‘ling.

$$22x-3=\frac{\log(1)}{\log(6)}$$

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

$$22x-3=\log_{6}\left(1\right)$$

3 ni tenglamaning ikkala tarafiga qo'shish.

$$22x=-\left(-3\right)$$

Ikki tarafini 22 ga bo‘ling.

$$x=\frac{3}{22}$$

x uchun yechish (complex solution)

$$x=\frac{i\pi n_{1}}{11\ln(6)}+\frac{3}{22}$$

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