What is the solution for the equation log2(x) + 4 = 416?

To solve the equation log₂(x) + 4 = 416, we first need to isolate the logarithmic term. We can do this by subtracting 4 from both sides of the equation:

log₂(x) = 416 – 4

This simplifies to:

log₂(x) = 412

Next, we will convert this logarithmic equation into its exponential form. Recall that if log_b(a) = c, then a = b^c. Here, b = 2, a = x, and c = 412.

Thus, we write:

x = 2⁴¹²

This indicates that to find the value of x, we need to calculate 2⁴¹². This is a very large number, specifically:

x ≈ 4.2 × 10¹²⁴ (using scientific notation for practicality).

In conclusion, the solution to the equation log₂(x) + 4 = 416 is:

x = 2⁴¹².