138*2^2x=46 eching

$$138 \cdot 2 ^ { 2 x } = 46$$

x uchun yechish

$$x=-\frac{\log_{2}\left(3\right)}{2}\approx -0,79248125$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$138\times 2^{2x}=46$$

Ikki tarafini 138 ga bo‘ling.

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

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

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

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

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

Ikki tarafini \log(2) ga bo‘ling.

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

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

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

Ikki tarafini 2 ga bo‘ling.

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

x uchun yechish (complex solution)

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

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