250000*106^x=297754 eching

$$250000 \times { 106 }^{ x } = 297754$$

x uchun yechish

$$x=3\log_{106}\left(\frac{53}{50}\right)\approx 0,037484509$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$250000\times 106^{x}=297754$$

Ikki tarafini 250000 ga bo‘ling.

$$106^{x}=\frac{148877}{125000}$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(106^{x})=\log(\frac{148877}{125000})$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$x\log(106)=\log(\frac{148877}{125000})$$

Ikki tarafini \log(106) ga bo‘ling.

$$x=\frac{\log(\frac{148877}{125000})}{\log(106)}$$

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

$$x=\log_{106}\left(\frac{148877}{125000}\right)$$

x uchun yechish (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(106)}+\log_{106}\left(\frac{148877}{125000}\right)$$

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