What is the true solution to the logarithmic equation below? log4[log4(2x]=1

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Question:

What is the true solution to the logarithmic equation below? log4[log4(2x]=1x=2
x=8
x=65
x=128

Answer:

1. 
write 1 as  so that we compare same base logarithms:

2. Neglect the equal bases and write the arguments:
 
So 

repeat step 1, that is write 4 as a logarithm with base 4: 

 

3. 

      
       
  

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