Solve log4(x+4) – 2 log4(x+1) =1/2 for x.  

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Solve `log_4(x+4)-2log_4(x+1)=1/2` .

First, simplify using logarithm rules:


Now exponeniate both sides with base 4:

`(x+4)/(x+1)^2=4^(1/2)` noting that `4^(1/2)=2` we cross-multiply:


So `x=1/2` or `x=-2` . But -2 is not in the domain of the original function.

Thus the solution is `x=1/2` .

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