15^t=16 eching

$$15 ^ { t } = 16$$

t uchun yechish

$$t=4\log_{15}\left(2\right)\approx 1,023832099$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$15^{t}=16$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(15^{t})=\log(16)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$t\log(15)=\log(16)$$

Ikki tarafini \log(15) ga bo‘ling.

$$t=\frac{\log(16)}{\log(15)}$$

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

$$t=\log_{15}\left(16\right)$$

t uchun yechish (complex solution)

$$t=\frac{2\pi n_{1}i}{\ln(15)}+4\log_{15}\left(2\right)$$

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