5=(1+96%)^n eching

$$5 = ( 1 + 96 \% ) ^ { n }$$

n uchun yechish

$$n = \frac{\log_{\frac{7}{5}} {(5)}}{2} \approx 2,391635531$$

Logaritm ifodasidan foydalanish qadamlari

\frac{96}{100} ulushini 4 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$5=\left(1+\frac{24}{25}\right)^{n}$$

\frac{49}{25} olish uchun 1 va \frac{24}{25}'ni qo'shing.

$$5=\left(\frac{49}{25}\right)^{n}$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$\left(\frac{49}{25}\right)^{n}=5$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(\left(\frac{49}{25}\right)^{n})=\log(5)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$n\log(\frac{49}{25})=\log(5)$$

Ikki tarafini \log(\frac{49}{25}) ga bo‘ling.

$$n=\frac{\log(5)}{\log(\frac{49}{25})}$$

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

$$n=\log_{\frac{49}{25}}\left(5\right)$$