(4/3)^x=(27/64) eching

$$( \frac { 4 } { 3 } ) ^ { x } = ( \frac { 27 } { 64 } )$$

x uchun yechish

$$x=-3$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$\left(\frac{4}{3}\right)^{x}=\frac{27}{64}$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(\left(\frac{4}{3}\right)^{x})=\log(\frac{27}{64})$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$x\log(\frac{4}{3})=\log(\frac{27}{64})$$

Ikki tarafini \log(\frac{4}{3}) ga bo‘ling.

$$x=\frac{\log(\frac{27}{64})}{\log(\frac{4}{3})}$$

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

$$x=\log_{\frac{4}{3}}\left(\frac{27}{64}\right)$$

x uchun yechish (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(\frac{4}{3})}+\log_{\frac{4}{3}}\left(\frac{27}{64}\right)$$

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