5*27^x=10935 eching

$$5 \times 27 ^ { x } = 10935$$

x uchun yechish

$$x = \frac{7}{3} = 2\frac{1}{3} \approx 2,333333333$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$5\times 27^{x}=10935$$

Ikki tarafini 5 ga bo‘ling.

$$27^{x}=2187$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(27^{x})=\log(2187)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$x\log(27)=\log(2187)$$

Ikki tarafini \log(27) ga bo‘ling.

$$x=\frac{\log(2187)}{\log(27)}$$

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

$$x=\log_{27}\left(2187\right)$$

x uchun yechish (complex solution)

$$x=\frac{2\pi n_{1}i}{3\ln(3)}+\frac{7}{3}$$

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