If $$4^{2n+1} = 2^{3n+9}$$​, then n = _____________.

Correct option is B

Given:

Given $$4^{2n+1} = 2^{3n+9}$$​​

Formula Used:

Surds and Indices

​$$(x^a)^b= x^{a\times b} = x^{ab}$$​​

Solution:

​$$4^{2n+1} = 2^{3n+9}$$​​

​$$(2^2)^{2n+1} = 2^{3n+9}$$​​

​$$2^{4n+2} = 2^{3n+9}$$​​

When bases are equal we equate the powers:

(4n + 2) = (3n + 9)

n = 7