{left(1+32/100right)}^x=200 eching

$${ \left(1+ \frac{ 32 }{ 100 } \right) }^{ x } =200$$

x uchun yechish

$$x=\log_{\frac{33}{25}}\left(200\right)\approx 19,083975886$$

Logaritm ifodasidan foydalanish qadamlari

\frac{32}{100} ulushini 4 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\left(1+\frac{8}{25}\right)^{x}=200$$

\frac{33}{25} olish uchun 1 va \frac{8}{25}'ni qo'shing.

$$\left(\frac{33}{25}\right)^{x}=200$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(\left(\frac{33}{25}\right)^{x})=\log(200)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$x\log(\frac{33}{25})=\log(200)$$

Ikki tarafini \log(\frac{33}{25}) ga bo‘ling.

$$x=\frac{\log(200)}{\log(\frac{33}{25})}$$

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

$$x=\log_{\frac{33}{25}}\left(200\right)$$

x uchun yechish (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(\frac{33}{25})}+\log_{\frac{33}{25}}\left(200\right)$$

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