100*2^4x=15 eching

$$100 \cdot 2 ^ { 4 x } = 15$$

x uchun yechish

$$x=\frac{\log_{2}\left(\frac{3}{5}\right)}{4}-\frac{1}{2}\approx -0,684241399$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$100\times 2^{4x}=15$$

Ikki tarafini 100 ga bo‘ling.

$$2^{4x}=\frac{3}{20}$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(2^{4x})=\log(\frac{3}{20})$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$4x\log(2)=\log(\frac{3}{20})$$

Ikki tarafini \log(2) ga bo‘ling.

$$4x=\frac{\log(\frac{3}{20})}{\log(2)}$$

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

$$4x=\log_{2}\left(\frac{3}{20}\right)$$

Ikki tarafini 4 ga bo‘ling.

$$x=\frac{\ln(\frac{3}{20})}{4\ln(2)}$$

x uchun yechish (complex solution)

$$x=\frac{\pi n_{1}i}{2\ln(2)}+\frac{\log_{2}\left(\frac{3}{20}\right)}{4}$$

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