4^2x-7=1/64 eching

$$4 ^ { 2 x - 7 } = \frac { 1 } { 64 }$$

x uchun yechish

$$x=2$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$4^{2x-7}=\frac{1}{64}$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(4^{2x-7})=\log(\frac{1}{64})$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$\left(2x-7\right)\log(4)=\log(\frac{1}{64})$$

Ikki tarafini \log(4) ga bo‘ling.

$$2x-7=\frac{\log(\frac{1}{64})}{\log(4)}$$

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

$$2x-7=\log_{4}\left(\frac{1}{64}\right)$$

7 ni tenglamaning ikkala tarafiga qo'shish.

$$2x=-3-\left(-7\right)$$

Ikki tarafini 2 ga bo‘ling.

$$x=\frac{4}{2}$$

x uchun yechish (complex solution)

$$x=\frac{i\pi n_{1}}{2\ln(2)}+2$$

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