52^2x+1=320 eching

$$52 ^ { 2 x + 1 } = 320$$

x uchun yechish

$$x=-\frac{\log_{52}\left(\frac{13}{80}\right)}{2}\approx 0,229937383$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$52^{2x+1}=320$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(52^{2x+1})=\log(320)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$\left(2x+1\right)\log(52)=\log(320)$$

Ikki tarafini \log(52) ga bo‘ling.

$$2x+1=\frac{\log(320)}{\log(52)}$$

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

$$2x+1=\log_{52}\left(320\right)$$

Tenglamaning ikkala tarafidan 1 ni ayirish.

$$2x=\log_{52}\left(320\right)-1$$

Ikki tarafini 2 ga bo‘ling.

$$x=\frac{\log_{52}\left(320\right)-1}{2}$$