128^x=5000 eching

$$128 ^ { x } = 5000$$

x uchun yechish

$$x = \frac{\log_{2} {(5000)}}{7} \approx 1,755387483$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$128^{x}=5000$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(128^{x})=\log(5000)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$x\log(128)=\log(5000)$$

Ikki tarafini \log(128) ga bo‘ling.

$$x=\frac{\log(5000)}{\log(128)}$$

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

$$x=\log_{128}\left(5000\right)$$

x uchun yechish (complex solution)

$$x=\frac{2\pi n_{1}i}{7\ln(2)}+\frac{\log_{2}\left(5000\right)}{7}$$

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