If log9 (3log2 (1 + log3 (1 + 2log2x))) = 1/2. Find the value of x.

Given that log9 (3log2 (1 + log3 (1 + 2log2x))) = 1/2.

We know that loga (a^x) = x. So, we can rewrite the equation as:

3log2 (1 + log3 (1 + 2log2x)) = 9^(1/2) 3log2 (1 + log3 (1 + 2log2x)) = 3

Divide both sides by 3:

log2 (1 + log3 (1 + 2log2x)) = 1

We know that loga (a^x) = x. So, we can rewrite the equation as:

1 + log3 (1 + 2log2x) = 2^1 log3 (1 + 2log2x) = 2 - 1 log3 (1 + 2log2x) = 1

We know that loga (a^x) = x. So, we can rewrite the equation as:

1 + 2log2x = 3^1 2log2x = 3 - 1 2log2x = 2

Divide both sides by 2:

log2x = 1

We know that loga (a^x) = x. So, we can rewrite the equation as:

x = 2^1 x = 2

Therefore, the value of x is 2.