3^x-2*3^x*3^-2=7 eching

$${ 3 }^{ x } -2 \times { 3 }^{ x } \times { 3 }^{ -2 } =7$$

x uchun yechish

$$x=2$$

Logaritm ifodasidan foydalanish qadamlari

-2 daraja ko‘rsatkichini 3 ga hisoblang va \frac{1}{9} ni qiymatni oling.

$$3^{x}-2\times 3^{x}\times \frac{1}{9}=7$$

\frac{2}{9} hosil qilish uchun 2 va \frac{1}{9} ni ko'paytirish.

$$3^{x}-\frac{2}{9}\times 3^{x}=7$$

\frac{7}{9}\times 3^{x} ni olish uchun 3^{x} va -\frac{2}{9}\times 3^{x} ni birlashtirish.

$$\frac{7}{9}\times 3^{x}=7$$

Ikki tarafini \frac{9}{7} va teskari kasri \frac{7}{9} ga ko‘paytiring.

$$3^{x}=7\times \frac{9}{7}$$

9 hosil qilish uchun 7 va \frac{9}{7} ni ko'paytirish.

$$3^{x}=9$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(3^{x})=\log(9)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$x\log(3)=\log(9)$$

Ikki tarafini \log(3) ga bo‘ling.

$$x=\frac{\log(9)}{\log(3)}$$

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

$$x=\log_{3}\left(9\right)$$

x uchun yechish (complex solution)

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

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