16^x=1/64 eching

$$16 ^ { x } = \frac { 1 } { 64 }$$

x uchun yechish

$$x = -\frac{3}{2} = -1\frac{1}{2} = -1,5$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$16^{x}=\frac{1}{64}$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

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

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

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

Ikki tarafini \log(16) ga bo‘ling.

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

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

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

x uchun yechish (complex solution)

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

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