Question

If 8^x × 4^y = 32 and 81^x ÷ 27^y = 3; find the values of x and y.

❗YOU CAN GIVE THE ANSWER
ON A SHEET OF PAPER ALSO!

Answer 1

Hey there,

➡8^x × 4^ y=32

➡2^(3x) × 2^ (2y)=2^5

➡2^(3x+2y)=2^5

Taking log with base 2,we get

➡3x+2y=5. ❇❇(I)❇❇

Also,

➡81^x/27^y=3

➡3^(4x-3y)=3^1

Taking log both sides with base 3,

➡4x-3y=1. ❇❇ II❇❇

Multiplying eq-(I) by 3 and (II) by 2

and adding we get

➡9x+6y+(8x-6y)=17

➡17 x =17

➡✔✔x=1 ,and y=1✔✔

Hope it helps.

✌✌

Answer 2

the first step :-

(2)^3×x + (2)^2×y = (2)^5