7(1/3)^x=63 eching

$$7 ( \frac { 1 } { 3 } ) ^ { x } = 63$$

x uchun yechish

$$x=-2$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$7\times \left(\frac{1}{3}\right)^{x}=63$$

Ikki tarafini 7 ga bo‘ling.

$$\left(\frac{1}{3}\right)^{x}=9$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(\left(\frac{1}{3}\right)^{x})=\log(9)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$x\log(\frac{1}{3})=\log(9)$$

Ikki tarafini \log(\frac{1}{3}) ga bo‘ling.

$$x=\frac{\log(9)}{\log(\frac{1}{3})}$$

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

$$x=\log_{\frac{1}{3}}\left(9\right)$$

x uchun yechish (complex solution)

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

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