Solve logarithmic equations with different bases?

You don't need to change base to solve this problem.

 

log 4 to base 4  =  1   and log 4 to base 16  is  1/2.          4^1 =4    and 16^1/2 =4

 

So x = 3/2

 

The question is testing your understanding of logs,rather than just being able to use them without really knowing the theory.

 

The base 16 log of 4   means what' power do I need to raise 16 to in order to get 4.' and since sqrt 16 =4  ,it's 1/2.

Remember that a logarithm is an index,that always helps if you are getting confused between base and index.