32^x+1=24 eching

$$32 ^ { x + 1 } = 24$$

x uchun yechish

$$x=\frac{\log_{2}\left(3\right)-2}{5}\approx -0,0830075$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$32^{x+1}=24$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(32^{x+1})=\log(24)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$\left(x+1\right)\log(32)=\log(24)$$

Ikki tarafini \log(32) ga bo‘ling.

$$x+1=\frac{\log(24)}{\log(32)}$$

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

$$x+1=\log_{32}\left(24\right)$$

Tenglamaning ikkala tarafidan 1 ni ayirish.

$$x=\frac{\log_{2}\left(24\right)}{5}-1$$

x uchun yechish (complex solution)

$$x=\frac{2\pi n_{1}i}{5\ln(2)}+\frac{\log_{2}\left(3\right)}{5}-\frac{2}{5}$$

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