10=100^8-5x eching

$$10 = 100 ^ { 8 - 5 x }$$

x uchun yechish

$$x = \frac{3}{2} = 1\frac{1}{2} = 1,5$$

Logaritm ifodasidan foydalanish qadamlari

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$100^{8-5x}=10$$

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$100^{-5x+8}=10$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(100^{-5x+8})=\log(10)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$\left(-5x+8\right)\log(100)=\log(10)$$

Ikki tarafini \log(100) ga bo‘ling.

$$-5x+8=\frac{\log(10)}{\log(100)}$$

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

$$-5x+8=\log_{100}\left(10\right)$$

Tenglamaning ikkala tarafidan 8 ni ayirish.

$$-5x=\frac{1}{2}-8$$

Ikki tarafini -5 ga bo‘ling.

$$x=-\frac{\frac{15}{2}}{-5}$$

x uchun yechish (complex solution)

$$x=-\frac{\pi n_{1}i\log(e)}{5}+\frac{3}{2}$$

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