(2/5)^x=125/8 eching

$$( \frac { 2 } { 5 } ) ^ { x } = \frac { 125 } { 8 }$$

x uchun yechish

$$x=-3$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$\left(\frac{2}{5}\right)^{x}=\frac{125}{8}$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(\left(\frac{2}{5}\right)^{x})=\log(\frac{125}{8})$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$x\log(\frac{2}{5})=\log(\frac{125}{8})$$

Ikki tarafini \log(\frac{2}{5}) ga bo‘ling.

$$x=\frac{\log(\frac{125}{8})}{\log(\frac{2}{5})}$$

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

$$x=\log_{\frac{2}{5}}\left(\frac{125}{8}\right)$$

x uchun yechish (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(\frac{2}{5})}+\log_{\frac{2}{5}}\left(\frac{125}{8}\right)$$

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