7^5x=32 eching

$$7 ^ { 5 x } = 32$$

x uchun yechish

$$x=\log_{7}\left(2\right)\approx 0,356207187$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$7^{5x}=32$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(7^{5x})=\log(32)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$5x\log(7)=\log(32)$$

Ikki tarafini \log(7) ga bo‘ling.

$$5x=\frac{\log(32)}{\log(7)}$$

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

$$5x=\log_{7}\left(32\right)$$

Ikki tarafini 5 ga bo‘ling.

$$x=\frac{5\log_{7}\left(2\right)}{5}$$

x uchun yechish (complex solution)

$$x=\frac{2\pi n_{1}i}{5\ln(7)}+\log_{7}\left(2\right)$$

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