(1/16)^2x=64 eching

$$( \frac { 1 } { 16 } ) ^ { 2 x } = 64$$

x uchun yechish

$$x=-\frac{3}{4}=-0,75$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$\left(\frac{1}{16}\right)^{2x}=64$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(\left(\frac{1}{16}\right)^{2x})=\log(64)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$2x\log(\frac{1}{16})=\log(64)$$

Ikki tarafini \log(\frac{1}{16}) ga bo‘ling.

$$2x=\frac{\log(64)}{\log(\frac{1}{16})}$$

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

$$2x=\log_{\frac{1}{16}}\left(64\right)$$

Ikki tarafini 2 ga bo‘ling.

$$x=-\frac{\frac{3}{2}}{2}$$

x uchun yechish (complex solution)

$$x=-\frac{i\pi n_{1}}{4\ln(2)}-\frac{3}{4}$$

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