What is the solution of log4x 616 = 4?

To solve the equation log₄x = 4, we can rewrite the logarithmic equation in its exponential form. The definition of a logarithm tells us that if log_ba = c, then b^c = a. Applying this to our equation:

Here, b = 4, c = 4, and a = x. Therefore:

4⁴ = x

Now we need to calculate 4⁴:

4⁴ = 4 × 4 × 4 × 4 = 256

Thus, we find that x = 256. To verify our solution, we can substitute this value back into the original logarithmic equation:

log₄256 = 4. Since 4⁴ = 256, the equation holds true.

Therefore, the solution to log₄x = 4 is x = 256.