4*10*8/32^-2=2^x+13 eching

$$\frac { 4 \times 10 \times 8 } { 32 ^ { - 2 } } = 2 ^ { x + 13 }$$

x uchun yechish

$$x=\log_{2}\left(5\right)+3\approx 5,321928095$$

Logaritm ifodasidan foydalanish qadamlari

40 hosil qilish uchun 4 va 10 ni ko'paytirish.

$$\frac{40\times 8}{32^{-2}}=2^{x+13}$$

320 hosil qilish uchun 40 va 8 ni ko'paytirish.

$$\frac{320}{32^{-2}}=2^{x+13}$$

-2 daraja ko‘rsatkichini 32 ga hisoblang va \frac{1}{1024} ni qiymatni oling.

$$\frac{320}{\frac{1}{1024}}=2^{x+13}$$

320 ni \frac{1}{1024} ga bo'lish 320 ga k'paytirish \frac{1}{1024} ga qaytarish.

$$320\times 1024=2^{x+13}$$

327680 hosil qilish uchun 320 va 1024 ni ko'paytirish.

$$327680=2^{x+13}$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$2^{x+13}=327680$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(2^{x+13})=\log(327680)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$\left(x+13\right)\log(2)=\log(327680)$$

Ikki tarafini \log(2) ga bo‘ling.

$$x+13=\frac{\log(327680)}{\log(2)}$$

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

$$x+13=\log_{2}\left(327680\right)$$

Tenglamaning ikkala tarafidan 13 ni ayirish.

$$x=\log_{2}\left(327680\right)-13$$

x uchun yechish (complex solution)

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

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