Question

If 3⁵ X 81² X 6561 = 3⁷, Then x = A -3 B 3 C -b D 1 by 3​

Answer 1

Correct Question : If (3^5x × 81^2 × 6561) ÷ 3^2x = 3^7 , then what is value of x ?

(A) 3, (B) -3, (C) 1/3, (D) -1/3

Solution :

Given that :

(3^5x × 81^2 × 6561) ÷ 3^2x = 3^7

[ We can write : 81 = 3^4 and 6561 = 3^8 ]

=> (3^5x × (3^4)^2 × 3^8) ÷ 3^2x = 3^7

=> (3^5x × 3^4×2 × 3^8) ÷ 3^2x = 3^7

=> (3^5x × 3^8 × 3^8) ÷ 3^2x = 3^7

As we know that : When bases are equal then powers will be added

=> (3^5x+8+8) ÷ 3^2x = 3^7

=> 3^(5x+16) ÷ 3^2x = 3^7

=> 3^(5x+16) × 3^(-2x) = 3^7

=> 3^(5x+16-2x) = 3^7

=> 3^(3x+16) = 3^7

As we know that : When bases are equal then powers will be equal too

=> 3x+16 = 7

=> 3x = 7-16

=> 3x = -9

=> x = -3

So, the value of x will be -3

Therefore the correct option will be Option (B).

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Hope it helps !!