94*2^frac{x{3}}=16 eching

$$94 \cdot 2 ^ { \frac { x } { 3 } } = 16$$

x uchun yechish

$$x=-3\log_{2}\left(47\right)+9\approx -7,663766555$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$94\times 2^{\frac{1}{3}x}=16$$

Ikki tarafini 94 ga bo‘ling.

$$2^{\frac{1}{3}x}=\frac{8}{47}$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(2^{\frac{1}{3}x})=\log(\frac{8}{47})$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$\frac{1}{3}x\log(2)=\log(\frac{8}{47})$$

Ikki tarafini \log(2) ga bo‘ling.

$$\frac{1}{3}x=\frac{\log(\frac{8}{47})}{\log(2)}$$

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

$$\frac{1}{3}x=\log_{2}\left(\frac{8}{47}\right)$$

Ikkala tarafini 3 ga ko‘paytiring.

$$x=\frac{-\log_{2}\left(47\right)+3}{\frac{1}{3}}$$

x uchun yechish (complex solution)

$$x=\frac{6\pi n_{1}i}{\ln(2)}-3\log_{2}\left(47\right)+9$$

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