3(13^x)=5 eching

$$3 ( 13 ^ { x } ) = 5$$

x uchun yechish

$$x=\log_{13}\left(\frac{5}{3}\right)\approx 0,199156222$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$3\times 13^{x}=5$$

Ikki tarafini 3 ga bo‘ling.

$$13^{x}=\frac{5}{3}$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(13^{x})=\log(\frac{5}{3})$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$x\log(13)=\log(\frac{5}{3})$$

Ikki tarafini \log(13) ga bo‘ling.

$$x=\frac{\log(\frac{5}{3})}{\log(13)}$$

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

$$x=\log_{13}\left(\frac{5}{3}\right)$$

x uchun yechish (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(13)}+\log_{13}\left(\frac{5}{3}\right)$$

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