70=90*3^-25x+50 eching

$$70 = 90 \times 3 ^ { - 25 x } + 50$$

x uchun yechish

$$x=\frac{-\log_{3}\left(2\right)+2}{25}\approx 0,05476281$$

Logaritm ifodasidan foydalanish qadamlari

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$90\times 3^{-25x}+50=70$$

Tenglamaning ikkala tarafidan 50 ni ayirish.

$$90\times 3^{-25x}=20$$

Ikki tarafini 90 ga bo‘ling.

$$3^{-25x}=\frac{2}{9}$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(3^{-25x})=\log(\frac{2}{9})$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$-25x\log(3)=\log(\frac{2}{9})$$

Ikki tarafini \log(3) ga bo‘ling.

$$-25x=\frac{\log(\frac{2}{9})}{\log(3)}$$

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

$$-25x=\log_{3}\left(\frac{2}{9}\right)$$

Ikki tarafini -25 ga bo‘ling.

$$x=\frac{\log_{3}\left(2\right)-2}{-25}$$

x uchun yechish (complex solution)

$$x=-\frac{2\pi n_{1}i}{25\ln(3)}-\frac{\log_{3}\left(2\right)}{25}+\frac{2}{25}$$

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