Agar $$ 2^{x}=3 $$ va $$ 18^{y}=72 $$ bo'lsa, $$ y $$ ni $$ x $$ orqali ifodalang.

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1. Dastlab $$ 2^{x}=3 $$ tenglamadan
   $$
   x=\frac{\ln 3}{\ln 2}
   $$
   deb yozish mumkin.

2. Ikkinchi tenglama $$ 18^{y}=72 $$ ni ko‘rib chiqamiz. Avvalo, sonlarni asosga ajratamiz:
   $$
   18=2\cdot 3^{2}, \quad 72=2^{3}\cdot 3^{2}.
   $$

3. Tenglamani quyidagicha yozamiz:
   $$
   \left(2\cdot 3^{2}\right)^{y}=2^{3}\cdot 3^{2}.
   $$
   Ekspansion qilamiz:
   $$
   2^{y}\cdot \left(3^{2}\right)^{y}=2^{3}\cdot 3^{2} \quad \Longrightarrow \quad 2^{y}\cdot 3^{2y}=2^{3}\cdot 3^{2}.
   $$

4. Logarifm olish orqali $$ y $$ ni ifodalash uchun har ikki tomonning logarifmini olamiz:
   $$
   \ln \left(2^{y}\cdot 3^{2y}\right)=\ln \left(2^{3}\cdot 3^{2}\right).
   $$

5. Logarifmning ko‘paytma uchun xususiyatlaridan foydalanib:
   $$
   y\ln 2 + 2y\ln 3 = 3\ln 2 + 2\ln 3.
   $$

6. $$ y $$-ni ajratamiz:
   $$
   y(\ln 2 + 2\ln 3) = 3\ln 2 + 2\ln 3,
   $$
   shundan
   $$
   y=\frac{3\ln 2+2\ln 3}{\ln 2+2\ln 3}.
   $$

7. Endi $$ \ln 3 $$ ni $$ x $$ bilan ifodalash uchun $$ 2^{x}=3 $$ tenglamadan
   $$
   \ln 3=x\ln 2,
   $$
   deb yozamiz.

8. Yuqoridagi ifodani $$ y $$ ga qo‘yamiz:
   $$
   y=\frac{3\ln 2+2(x\ln 2)}{\ln 2+2(x\ln 2)}=\frac{\ln 2(3+2x)}{\ln 2(1+2x)}.
   $$

9. Natijada, $$ \ln 2 $$ qisqaradi va quyidagini olamiz:
   $$
   y=\frac{3+2x}{1+2x}.
   $$

Shunday qilib, $$ y $$ ni $$ x $$ orqali ifodalash:
$$
y=\frac{3+2x}{1+2x}.
$$
$$ y = \frac{3 + 2x}{1 + 2x} $$

Agar va bo’lsa, ni orqali
ifodalang.

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Agar va bo’lsa, ni orqali ifodalang.