32^3x-2-48=0 eching

$$32 ^ { 3 x - 2 } - 48 = 0$$

x uchun yechish

$$x = \frac{\log_{2} {(3)} + 14}{15} \approx 1,0389975$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$32^{3x-2}-48=0$$

48 ni tenglamaning ikkala tarafiga qo'shish.

$$32^{3x-2}=48$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(32^{3x-2})=\log(48)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$\left(3x-2\right)\log(32)=\log(48)$$

Ikki tarafini \log(32) ga bo‘ling.

$$3x-2=\frac{\log(48)}{\log(32)}$$

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

$$3x-2=\log_{32}\left(48\right)$$

2 ni tenglamaning ikkala tarafiga qo'shish.

$$3x=\frac{\log_{2}\left(48\right)}{5}-\left(-2\right)$$

Ikki tarafini 3 ga bo‘ling.

$$x=\frac{\frac{\log_{2}\left(48\right)}{5}+2}{3}$$

x uchun yechish (complex solution)

$$x=\frac{2\pi n_{1}i}{15\ln(2)}+\frac{\log_{2}\left(3\right)}{15}+\frac{14}{15}$$

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