(2^3x-1+10)div7=6 eching

$$( 2 ^ { 3 x - 1 } + 10 ) \div 7 = 6$$

x uchun yechish

$$x=2$$

Logaritm ifodasidan foydalanish qadamlari

Ikkala tarafini 7 ga ko‘paytiring.

$$2^{3x-1}+10=6\times 7$$

42 hosil qilish uchun 6 va 7 ni ko'paytirish.

$$2^{3x-1}+10=42$$

Tenglamaning ikkala tarafidan 10 ni ayirish.

$$2^{3x-1}=32$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(2^{3x-1})=\log(32)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$\left(3x-1\right)\log(2)=\log(32)$$

Ikki tarafini \log(2) ga bo‘ling.

$$3x-1=\frac{\log(32)}{\log(2)}$$

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

$$3x-1=\log_{2}\left(32\right)$$

1 ni tenglamaning ikkala tarafiga qo'shish.

$$3x=5-\left(-1\right)$$

Ikki tarafini 3 ga bo‘ling.

$$x=\frac{6}{3}$$

x uchun yechish (complex solution)

$$x=\frac{2\pi n_{1}i}{3\ln(2)}+2$$

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