15^9x=4 eching

$$15 ^ { 9 x } = 4$$

x uchun yechish

$$x=\frac{2\log_{15}\left(2\right)}{9}\approx 0,056879561$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$15^{9x}=4$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(15^{9x})=\log(4)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$9x\log(15)=\log(4)$$

Ikki tarafini \log(15) ga bo‘ling.

$$9x=\frac{\log(4)}{\log(15)}$$

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

$$9x=\log_{15}\left(4\right)$$

Ikki tarafini 9 ga bo‘ling.

$$x=\frac{2\log_{15}\left(2\right)}{9}$$

x uchun yechish (complex solution)

$$x=\frac{2\pi n_{1}i}{9\ln(15)}+\frac{2\log_{15}\left(2\right)}{9}$$

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