3(5^3x+1)=36 eching

$$3 ( 5 ^ { 3 x + 1 } ) = 36$$

x uchun yechish

$$x=\frac{\log_{5}\left(12\right)-1}{3}\approx 0,18131977$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$3\times 5^{3x+1}=36$$

Ikki tarafini 3 ga bo‘ling.

$$5^{3x+1}=12$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(5^{3x+1})=\log(12)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$\left(3x+1\right)\log(5)=\log(12)$$

Ikki tarafini \log(5) ga bo‘ling.

$$3x+1=\frac{\log(12)}{\log(5)}$$

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

$$3x+1=\log_{5}\left(12\right)$$

Tenglamaning ikkala tarafidan 1 ni ayirish.

$$3x=\log_{5}\left(12\right)-1$$

Ikki tarafini 3 ga bo‘ling.

$$x=\frac{\log_{5}\left(12\right)-1}{3}$$

x uchun yechish (complex solution)

$$x=\frac{2\pi n_{1}i}{3\ln(5)}+\frac{\log_{5}\left(12\right)}{3}-\frac{1}{3}$$

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