If log_2(log_3(log_4(x))) = 1, what is the value of x?
Correct: D
We are given the equation log_2(log_3(log_4(x))) = 1.
We will solve this by repeatedly applying the definition of logarithms: if log_b(a) = c, then a = b^c.
Step 1: Apply the definition for the outermost logarithm (base 2):
log_3(log_4(x)) = 2^1
log_3(log_4(x)) = 2
Step 2: Apply the definition for the next logarithm (base 3):
log_4(x) = 3^2
log_4(x) = 9
Step 3: Apply the definition for the innermost logarithm (base 4):
x = 4^9
To simplify 4^9, we can express 4 as 2^2:
x = (2^2)^9
x = 2^(2 * 9)
x = 2^18.
The value of x is 2^18.