(33^7)^4/3^3=3^5*x eching

$$\frac { ( 33 ^ { 7 } ) ^ { 4 } } { 3 ^ { 3 } } = 3 ^ { 5 \cdot x }$$

x uchun yechish

$$x=\frac{28\log_{3}\left(11\right)}{5}+5\approx 17,222886696$$

Logaritm ifodasidan foydalanish qadamlari

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. 7 va 4 ni ko‘paytirib, 28 ni oling.

$$\frac{33^{28}}{3^{3}}=3^{5x}$$

28 daraja ko‘rsatkichini 33 ga hisoblang va 3299060778251569566188233498374847942355841 ni qiymatni oling.

$$\frac{3299060778251569566188233498374847942355841}{3^{3}}=3^{5x}$$

3 daraja ko‘rsatkichini 3 ga hisoblang va 27 ni qiymatni oling.

$$\frac{3299060778251569566188233498374847942355841}{27}=3^{5x}$$

122187436231539613562527166606475849716883 ni olish uchun 3299060778251569566188233498374847942355841 ni 27 ga bo‘ling.

$$122187436231539613562527166606475849716883=3^{5x}$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$3^{5x}=122187436231539613562527166606475849716883$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(3^{5x})=\log(122187436231539613562527166606475849716883)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$5x\log(3)=\log(122187436231539613562527166606475849716883)$$

Ikki tarafini \log(3) ga bo‘ling.

$$5x=\frac{\log(122187436231539613562527166606475849716883)}{\log(3)}$$

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

$$5x=\log_{3}\left(122187436231539613562527166606475849716883\right)$$

Ikki tarafini 5 ga bo‘ling.

$$x=\frac{\log_{3}\left(122187436231539613562527166606475849716883\right)}{5}$$

x uchun yechish (complex solution)

$$x=\frac{2\pi n_{1}i}{5\ln(3)}+\frac{28\log_{3}\left(11\right)}{5}+5$$

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