If 3ˣ × 9¹⁵ × 27⁶ = 81¹⁶, then the value of x is:

Correct option is C

Given:

If 3^x × 9¹⁵ × 27⁶ = 81¹⁶

Formula Used:

a^m = aⁿ, m = n

a^m × aⁿ = a^{(m + n)}

Solution:

3^x × 9¹⁵ × 27⁶ = 81¹⁶

=> 3^x × (3²)¹⁵ × (3³)⁶ = (3⁴)¹⁶

=> 3^{(x + 30 + 18)} = 3⁶⁴

=> x + 30 + 18 = 64

=> x = 16

∴ The Value of x is 16.