22=9^4x-3 eching

$$22 = 9 ^ { 4 x - 3 }$$

x uchun yechish

$$x = \frac{\log_{3} {(22)} + 6}{8} \approx 1,101698512$$

Logaritm ifodasidan foydalanish qadamlari

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$9^{4x-3}=22$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(9^{4x-3})=\log(22)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$\left(4x-3\right)\log(9)=\log(22)$$

Ikki tarafini \log(9) ga bo‘ling.

$$4x-3=\frac{\log(22)}{\log(9)}$$

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

$$4x-3=\log_{9}\left(22\right)$$

3 ni tenglamaning ikkala tarafiga qo'shish.

$$4x=\frac{\log_{3}\left(22\right)}{2}-\left(-3\right)$$

Ikki tarafini 4 ga bo‘ling.

$$x=\frac{\frac{\log_{3}\left(22\right)}{2}+3}{4}$$

x uchun yechish (complex solution)

$$x=\frac{\pi n_{1}i}{4\ln(3)}+\frac{\log_{3}\left(22\right)}{8}+\frac{3}{4}$$

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