Question

(3n *9^n+1) ÷ (3^n-1 X 27^n-1) = 81​

Find the value of n

Answer 1

The value of n is 4.

Step-by-step explanation:

Since we have given that

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

We need to find the value of n.

So, we will rewrite it as follows:

$\dfrac{3^n\times 3^{2(n+1)}}{3^{n-1}\times 3^{3(n-1)}}=81\\\\\dfrac{3^n\times 3^{2n+2}}{3^{n-1}\times 3^{3n-9}}=81\\\\\dfrac{3^{n+2n+2}}{3^{n-1+3n-9}}=81\\\\\dfrac{3^{3n+2}}{3^{4n-10}}=3^4\\\\3^{3n+2-(4n-10)}=3^4\\\\\text{Comparing the powers as their base is same}\\\\3n+2-4n+10=4\\\\-n+8=4\\\\-n=4-8\\\\-n=-4\\\\n=4$

Hence, the value of n is 4.

# learn more:

(3^n×9^n+1)÷(3^n-1×27^n-1)=81

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