8^6y+4=64 eching

$$8 ^ { 6 y + 4 } = 64$$

y uchun yechish

$$y=-\frac{1}{3}\approx -0,333333333$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$8^{6y+4}=64$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(8^{6y+4})=\log(64)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$\left(6y+4\right)\log(8)=\log(64)$$

Ikki tarafini \log(8) ga bo‘ling.

$$6y+4=\frac{\log(64)}{\log(8)}$$

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

$$6y+4=\log_{8}\left(64\right)$$

Tenglamaning ikkala tarafidan 4 ni ayirish.

$$6y=2-4$$

Ikki tarafini 6 ga bo‘ling.

$$y=-\frac{2}{6}$$

y uchun yechish (complex solution)

$$y=\frac{\pi n_{1}i}{9\ln(2)}-\frac{1}{3}$$

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