5*3^1-x=45 eching

$$5 \times { 3 }^{ 1-x } =45$$

x uchun yechish

$$x=-1$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$5\times 3^{-x+1}=45$$

Ikki tarafini 5 ga bo‘ling.

$$3^{-x+1}=9$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(3^{-x+1})=\log(9)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$\left(-x+1\right)\log(3)=\log(9)$$

Ikki tarafini \log(3) ga bo‘ling.

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

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

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

Tenglamaning ikkala tarafidan 1 ni ayirish.

$$-x=2-1$$

Ikki tarafini -1 ga bo‘ling.

$$x=\frac{1}{-1}$$

x uchun yechish (complex solution)

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

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