6*2^frac{x{4}}=222 eching

$$6 \cdot 2 ^ { \frac { x } { 4 } } = 222$$

x uchun yechish

$$x=4\log_{2}\left(37\right)\approx 20,837813463$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$6\times 2^{\frac{1}{4}x}=222$$

Ikki tarafini 6 ga bo‘ling.

$$2^{\frac{1}{4}x}=37$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(2^{\frac{1}{4}x})=\log(37)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$\frac{1}{4}x\log(2)=\log(37)$$

Ikki tarafini \log(2) ga bo‘ling.

$$\frac{1}{4}x=\frac{\log(37)}{\log(2)}$$

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

$$\frac{1}{4}x=\log_{2}\left(37\right)$$

Ikkala tarafini 4 ga ko‘paytiring.

$$x=\frac{\log_{2}\left(37\right)}{\frac{1}{4}}$$

x uchun yechish (complex solution)

$$x=\frac{8\pi n_{1}i}{\ln(2)}+4\log_{2}\left(37\right)$$

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