Question

(3n *9^n+1) ÷ (3^n-1 X 27^n-1) = 81​

Answer 1

The value of n is 2.

Step-by-step explanation:

$(3^{n} \times 9^{(n+1)})$ ÷ $(3^{(n-1)} \times 27^{(n-1)} ) = 81$

=> $(3^{n} \times 3^{2(n+1)} )$ ÷ $(3^{(n-1)} \times 3^{3(n-1)} ) = 81$

=>  $(3^{n} \times 3^{2n + 2} )$ ÷ $(3^{n-1} \times 3^{3n - 3} ) = 81$

=> $(3^{2n + 2+n} )$ ÷ $(3^{ n -1 + 3n - 3} ) = 81$

=> $(3^{3n+2} )$ ÷ $(3^{4n - 4} )$ = 81

=> $3^{3n+2-4n+4} = 81$

=> $3^{-n+6} = 3^{4}$

Base of the two sides is 3.

So, -n + 6 = 4

=> n = 6 - 4 = 2

Hence, the value of n is 2.

Answer 2

Answer:The value of n is 2

Step-by-step explanation:

(3^{n} \times 9^{(n+1)}) ÷ (3^{(n-1)} \times 27^{(n-1)} ) = 81

=> (3^{n} \times 3^{2(n+1)} ) ÷ (3^{(n-1)} \times 3^{3(n-1)} ) = 81

=> (3^{n} \times 3^{2n + 2} ) ÷ (3^{n-1} \times 3^{3n - 3} ) = 81

=> (3^{2n + 2+n} ) ÷ (3^{ n -1 + 3n - 3} ) = 81

=> (3^{3n+2} ) ÷ (3^{4n - 4} ) = 81

=> 3^{3n+2-4n+4} = 81

=> 3^{-n+6} = 3^{4}

Base of the two sides is 3.

So, -n + 6 = 4

=> n = 6 - 4 = 2

Hence, the value of n is 2.