If 3 to the power of x+1 = 81 and 81 to the power of x-y = 3 then what is the value of x and y?

From 1st condition:

3^ (x+1) = 81

Take log on both sides,

➡ log [3^ (x+1) ]=log81

Use the property: log (x^a) = a logx

➡ (x+1) log 3=log (3⁴)

➡ (x+1) log 3=4*log 3

➡ (x+1) = 4 (log 3 / log 3)

➡ x+1=4

➡ x=3➡↪➡↪ ANS

From 2nd condition, (Same process are repeated)

81^ (x-y) = 3

➡ 3^4 (x-y) = 3

➡ log [3^4 (3-y) ]=log 3

➡ 4 (3-y) log 3=log 3

➡ (3-y) = (log 3) / (4log 3)

➡ 3-y = (1/4)

➡ y=11/4 ➡↪➡↪ ANS