15^3x-4=10 eching

$$15 ^ { 3 x - 4 } = 10$$

x uchun yechish

$$x = \frac{\log_{15} {(506250)}}{3} \approx 1,616758051$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$15^{3x-4}=10$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(15^{3x-4})=\log(10)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$\left(3x-4\right)\log(15)=\log(10)$$

Ikki tarafini \log(15) ga bo‘ling.

$$3x-4=\frac{\log(10)}{\log(15)}$$

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

$$3x-4=\log_{15}\left(10\right)$$

4 ni tenglamaning ikkala tarafiga qo'shish.

$$3x=\log_{15}\left(10\right)-\left(-4\right)$$

Ikki tarafini 3 ga bo‘ling.

$$x=\frac{\log_{15}\left(10\right)+4}{3}$$

x uchun yechish (complex solution)

$$x=\frac{2\pi n_{1}i}{3\ln(15)}+\frac{\log_{15}\left(506250\right)}{3}$$

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