(1/2)^x=6 eching

$$( \frac { 1 } { 2 } ) ^ { x } = 6$$

x uchun yechish

$$x=-\log_{2}\left(6\right)\approx -2,584962501$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$\left(\frac{1}{2}\right)^{x}=6$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(\left(\frac{1}{2}\right)^{x})=\log(6)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$x\log(\frac{1}{2})=\log(6)$$

Ikki tarafini \log(\frac{1}{2}) ga bo‘ling.

$$x=\frac{\log(6)}{\log(\frac{1}{2})}$$

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

$$x=\log_{\frac{1}{2}}\left(6\right)$$

x uchun yechish (complex solution)

$$x=-\frac{2\pi n_{1}i}{\ln(2)}-\log_{2}\left(6\right)$$

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