2400/1200=(109/100)^x eching

$$\frac { 2400 } { 1200 } = ( \frac { 109 } { 100 } ) ^ { x }$$

x uchun yechish

$$x=\log_{\frac{109}{100}}\left(2\right)\approx 8,043231727$$

Logaritm ifodasidan foydalanish qadamlari

2 ni olish uchun 2400 ni 1200 ga bo‘ling.

$$2=\left(\frac{109}{100}\right)^{x}$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$\left(\frac{109}{100}\right)^{x}=2$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(\left(\frac{109}{100}\right)^{x})=\log(2)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$x\log(\frac{109}{100})=\log(2)$$

Ikki tarafini \log(\frac{109}{100}) ga bo‘ling.

$$x=\frac{\log(2)}{\log(\frac{109}{100})}$$

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

$$x=\log_{\frac{109}{100}}\left(2\right)$$

x uchun yechish (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(\frac{109}{100})}+\log_{\frac{109}{100}}\left(2\right)$$

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