If 9 n × 3 2 × 3 n − (27) n 3 3 5 × 2 3 = 1 27 , then what is the value of n? - Sri Chaitanya Infinity Learn Best Online Courses for NCERT Solutions, CBSE, ICSE, JEE, NEET, Olympiad and Class 6 to 12

Given expression is

9 n × 32 × 3 n − (27) n 335 × 23 = 127

.
Breaking it into exponential form.

32 n × 32 × 3 n − 33 n 315 × 23 = 127

Using

a m × a n = a m + n

3 (3 n) × 32 − 3 3 n 315 × 23 = 127

Taking common

3 3 n

3 3 n 32 − 1 315 × 23 = 127

3 3 n (9 − 1) 315 × 23 = 127

3 3 n (8) 315 × 23 = 127

3 3 n × 23 315 × 23 = 127

3 3 n 315 = 133

Applying

a m ÷ a n = a m − n

3 3 n − 15 = 3 − 3

Comparing the exponents, we get,

3 n − 15 = − 3

3 n = − 3 + 15

3 n = 12

n = 4

The value of n is 4.
Therefore, the correct option is 1.

If $9 n × 32 × 3 n − (27) n 335 × 23 = 127$ , then what is the value of n?