What is the solution of log3(x)2 = 4096?

To find the value of x in the logarithmic equation log3(x) = 2 and the equality 2 = 4096, we first understand that having logb(a) = c can be rewritten as a = bc.

In this case, we convert the logarithmic equation to its exponential form:

x = 32

Calculating that gives:

x = 9

Now let’s consider the other part of the question which states 2 = 4096. It seems there may be some misunderstanding here, as 2 cannot equal 4096. However, we can compute the value of log3(4096) to see if it relates to our initial equation. Since 4096 can be rewritten as 212, we compute:

log₃(4096) = log₃(2¹²) = 12 * log₃(2)

Ultimately, the original equation log3(x) = 2 has a straightforward solution of:

x = 9