(2/7)^-3*(2/7)^-11=(2/7)^x eching

$$( \frac { 2 } { 7 } ) ^ { - 3 } \times ( \frac { 2 } { 7 } ) ^ { - 11 } = ( \frac { 2 } { 7 } ) ^ { x }$$

x uchun yechish

$$x=-14$$

Logaritm ifodasidan foydalanish qadamlari

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. -3 va -11 ni qo‘shib, -14 ni oling.

$$\left(\frac{2}{7}\right)^{-14}=\left(\frac{2}{7}\right)^{x}$$

-14 daraja ko‘rsatkichini \frac{2}{7} ga hisoblang va \frac{678223072849}{16384} ni qiymatni oling.

$$\frac{678223072849}{16384}=\left(\frac{2}{7}\right)^{x}$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$\left(\frac{2}{7}\right)^{x}=\frac{678223072849}{16384}$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(\left(\frac{2}{7}\right)^{x})=\log(\frac{678223072849}{16384})$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$x\log(\frac{2}{7})=\log(\frac{678223072849}{16384})$$

Ikki tarafini \log(\frac{2}{7}) ga bo‘ling.

$$x=\frac{\log(\frac{678223072849}{16384})}{\log(\frac{2}{7})}$$

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

$$x=\log_{\frac{2}{7}}\left(\frac{678223072849}{16384}\right)$$

x uchun yechish (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(\frac{2}{7})}+2\log_{\frac{2}{7}}\left(\frac{823543}{128}\right)$$

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