Which of the following shows the true solution to the logarithmic equation below? log4[log4 (2x) ]=1

Answer: 128

The log is base 4. To undo the log, we raise both sides as exponents and the base will be 4.

So log (4, y) = 1 turns into y = 4^1 and it becomes y = 4

Replace y with log (4,2x) and we end up with log (4,2x) = 4

Repeat the step of raising both sides as exponents to get 2x = 4^4 leading to 2x = 256

The last step is to divide both sides by 2, which is why the answer is x = 128.