4845=123^x eching

$$4845 = { 123 }^{ x }$$

x uchun yechish

$$x=\log_{123}\left(4845\right)\approx 1,76337852$$

Logaritm ifodasidan foydalanish qadamlari

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$123^{x}=4845$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(123^{x})=\log(4845)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$x\log(123)=\log(4845)$$

Ikki tarafini \log(123) ga bo‘ling.

$$x=\frac{\log(4845)}{\log(123)}$$

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

$$x=\log_{123}\left(4845\right)$$

x uchun yechish (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(123)}+\log_{123}\left(4845\right)$$

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